









5<k 





^°^ 








W 














\b, »o.,« A <. *'TT«* «G V 




P..'J&±'.\. <*.>££*.% *+..'J&i.S. c"*.c^:.* o >\. 











V* V 
W 1 .*tfta W .vriMfc V> 










v><b- 







O K 



* A <* *^T77* .g v 






^. ^ 













"^o 4 * 

^°^ 










^°^ 
















^ # * A 



* ^ 







»1V« «> 



A v 



,0 



















*, ^ °^ * • - • 





VV 




-j»V 









' <v* 




*> V* '•*• • "° A v ' 





























** v % 






^d* 







'bV" 















,v^ 



> ^ 



lV>^ 











i^ . K • - *rt .V 0* • , 



4 O 



^°* 

















IC 8941 



Bureau of Mines Information Circular/1983 




Field Determinations of a Probabilistic 
Density Function for Slope Stability 
Analysis of Tailings Embankments 

By P. C. McWilliams and D. R. Tesarik 




UNITED STATES DEPARTMENT OF THE INTERIOR 



Information Circular 8941 

1 

Field Determinations of a Probabilistic 
Density Function for Slope Stability 
Analysis of Tailings Embankments 

By P. C. McWilliams and D. R. Tesarik 




UNITED STATES DEPARTMENT OF THE INTERIOR 

James G. Watt, Secretary 

BUREAU OF MINES 
Robert C. Horton, Director 




<A 



\M ^ 



\ 



>A 



0' 



This publication has been cataloged as follows: 



McWilliams, P. C. (Paul C.) 

Field determinations of a probabilistic density function for slope 
stability analysis of tailings embankments. 

(Information circular / Bureau of Mines ; 8941) 

Bibliography: p. 13. 

Supt. of Docs, no.: I 28.27:8941. 

1. Spoil banks— Safety measures. 2. Tailings dams— Safety mea- 
sures. 3. Slopes (Soil mechanics). 4. Soil mechanics— Statistical 
methods. 5. Probabilities. I. Tesarik, D. R. (Douglas R.). II. Title. 
III. Series: Information circular (United States. Bureau of Mines) ; 
8941. 

-W295.U4 622s [622.7] 83-600123 



CONTENTS 



Page 



Abstract 1 

Introduction 2 

Acknowledgments 2 

Probabilistic approach 2 

Propagation of error 3 

Distribution properties 5 

Propagation of error applied to the data 9 

Confidence interval for the factor of safety 9 



X 



Geotechnical innovation and probabilistic modeling 10 

Conclusions 12 

References 13 

Appendix. — Data collection, slope stability, and laboratory testing 14 

ILLUSTRATIONS 

a! 
\l 

1. Slip circle factor of safety formulation 2 

2. Concept of probability of failure 3 

3. Factor of safety histograms 7 

4. Internal friction angle histograms 7 

5. Cohesion histograms 7 

6. Soil density histograms 7 

7. Ninety-five percent confidence interval — factor of safety, CDA Mine — with 

varying sample size 11 

8. Ninety-five percent confidence interval — factor of safety, SW Mine — with 

varying sample size 11 

9. Variance reduction applied to spatially oriented shear strength values... 12 

A-l. SW data station pattern 15 

A-2. Idealized profile — SW embankment 16 

A-3. Range of grain-size curves for CDA data 17 

TABLES 

1. Basic statistics for soil parameters 4 

2. Three model curve fits to Fellenius 1 factor of safety 6 

3. Normal curve-fit parameters for <j), c, y, and F 8 

4. Comparison of coefficient of variation estimates for Fellenius' factor of 

safety 9 

5. Correlation coefficients 9 

A-l. CDA laboratory data 18 

A-2 . SW laboratory data 26 








UNIT OF 


MEASURE 


ABBREVIATIONS USED 


IN THIS REPORT 


deg 


degree 




mm/sec 


millimeter per second 


ft 


foot 




pcf 


pound per cubic foot 


in 


inch 




pet 


percent 


mm 


millimeter 


psi 


pound per square inch 



FIELD DETERMINATIONS OF A PROBABILISTIC DENSITY FUNCTION 
FOR SLOPE STABILITY ANALYSIS OF TAILINGS EMBANKMENTS 

By P. C. McWilliams 1 and D. R. Tesarik 2 



ABSTRACT 

Theoreticians in soil mechanics have been pursuing a probabilistic 
approach to the factor of safety of an embankment or dam for the past 
10 years. The motivation for this work is in contrast to the current 
practice of deterministically computing a factor of safety and treating 
it as an absolute with no regard to its inherent statistical 
variability. 

Basic to the probabilistic approach is the selection of an appropri- 
ate statistical model to represent the histogram or probability density 
function (PDF) of the factor of safety values. Rather than simply as- 
suming which PDF is appropriate, the Bureau of Mines collected data at 
two waste disposal embankments for consideration. This report ad- 
dresses three candidate models, using the techniques of nonlinear curve 
fitting, and identifies the "best" model. A propagation of error for- 
mula for estimating the variability of Fellenius' factor of safety is 
also discussed. 



Mathematical statistician. 



1 

2 Mathematician. 
Both authors are with the Spokane Research Center, Bureau of Mines, Spokane, Wash. 



INTRODUCTION 



Theoreticians in soil mechanics have 
been pursuing a probabilistic approach 
to the factor of safety of an embank- 
ment or dam for the past 10 years. The 
motivation for this work is in contrast 
to the current practice of deterministi- 
cally computing a factor of safety and 
treating it as an absolute with no re- 
gard to its inherent statistical vari- 
ability. Stated simply, in the past, 
soils engineers have used a single pa- 
rameter, the factor of safety. It would 
now seem prudent to impose an additional 
parameter, the dispersion of the fac- 
tor of safety. Given these two param- 
eters, one may then compute the proba- 
bility of failure as a measure of slope 
stability. 



Basic to the probabilistic approach is 
the selection of an appropriate statisti- 
cal model to represent the histogram or 
probability density function (PDF) of the 
factor of safety values. It is certainly 
easy to hypothesize such a model; the 
normal PDF is almost always the first 
choice. For this reason, the Bureau of 
Mines collected data at two waste dis- 
posal embankments such that their PDF's 
could be investigated. This report is 
addressed to investigating candidate mod- 
els via the techniques of nonlinear curve 
fitting, and then choosing the "best" 
model available. A propagation of error 
formula for estimating the variability 
of Fellenius' factor of safety is also 
discussed. 



ACKNOWLEDGMENTS 



The authors would like to thank Lynn and careful 
Atkins and Joe Jucha for their persistent data. 



testing of this large set of 



PROBABILISTIC APPROACH 



There are several prior discussions of 
applying probability theory to slope sta- 
bility analysis (l_-2, ]_, .12, 15-16, ). 3 
For orientation purposes, it would seem 
prudent to briefly sketch the problem. 
Most dam design engineers use the methods 
of either Bishop-Morgenstern or Fellenius 
(_5_, 7_, 9) to compute the factor of safety 
for slope stability design. These tech- 
niques are deterministic in that one val- 
ue is computed which measures the "safety 
of the dam." The basic postulate is that 
of a potential slip-circle failure. In 
terms of moments, the factor of safety is 
the ratio of the resisting moment to the 
overturning moment of the embankment 
(fig. 1). If this ratio is greater than 
1, the structure is assumed to be in a 
nonfailure state. Often there are so- 
called rules of practice; for example, 
a factor of safety of 1.5 or greater is 
required in some applications. 

3 Underlined numbers in parentheses re- 
fer to items in the list of references 
preceding the appendix. 



The probabilistic approach suggests 
that in addition to computing the fac- 
tor of safety, one should also include 
its variability. One such approach is 
to calculate a confidence interval for 
the factor of safety by collecting sev- 
eral samples and applying the theorem 
that a mean value (in this case, the 
average factor of safety value) is 
normally distributed (8). This is dis- 
cussed in detail in the section entitled 
"Confidence Interval for the Factor of 



r- 


— __ _ 


~-5 a 


dius 






/ 
/ 


~~~~---_ 


/ 




/ 




/ 






/ 








/ 










/ . 








/ 






/ W 








>^ 


Si N 

s 




«\| 


w. 


FIGURE 1. - 


Slip circle \ 


formulation 


. 











KEY 



th 



= Weight of i ln slice 

= Normal force, i ,h slice 

= Resisting shear force 



Safety." A necessary ingredient in most 
probabilistic work is the assumption of a 
PDF that characterizes a population of 
factor of safety values. 

Another approach is to compute the 
probability of failure, which is repre- 
sented by the area under the PDF to the 
left of the value 1 (fig. 2). The main 
objective of this report was to collect 
enough sample values from two tailings 



embankments to establish the PDF for the 
factor of safety values. In practice, it 
would not be expedient to expend the time 
and money to collect the necessary number 
of samples required to derive the PDF. 
Work such as that done herein should pro- 
vide some assurance that it would not be 
unreasonable to postulate a particular 
PDF without actually collecting a partic- 
ularly large sample of data. 



PROPAGATION OF ERROR 4 



An interesting alternative to collect- 
ing enough samples to establish a PDF 
is to apply the statistical technique 
known as propagation of error (6). This 
technique will approximate the standard 
deviation of the factor of safety (sp). 
It may not be convenient for the designer 
to collect enough data to compute Sp di- 
rectly; he or she may instead assume 
values for the coefficient of variation 
for the soil properties — and then apply 
propagation of error. Reference is 
invited to either Lee and Singh ( 11 ) or 
table 1 of this paper for candidate co- 
efficient of variation values. 



Mathematical 
follows: 



considerations 



are as 



Given a function of several variables, 



G = G (a, b, c), 



(1) 



4 There 
between 



exist 
the 



notational 
disciplines 



ambiguities 
of the 



mathematicians-statisticians and that of 



the geotechnical engineers, 
per, deference is given to 



In this pa- 
the notation 



of mathematics and statistics. 









KEY 








F = Factor of safety 








F = Mean factor 








of safety 








s F = Standard deviation 






/\ 


of F 






A 


l F c = Critical factor 


Probability / 




! / 


\ of safety 


of fa 

i 


i 1 u r e / 


^s F -^ 


/ 

Distribution 


of F >v 



F c = 1 . F 

FIGURE 2. - Concept of probability of failure, 



by propagation of error, the variance of G (s G ), is given by 



Sg = G a s a + G b s b + G c s c + 2r ab G a G b s a s b 
+ 2r ac G a G c s a s c + 2r bc G b G c s c s b , 
where G\ = partial derivative of G with respect to the i"^ parameter, 



(2) 



and 



S| = variance of the i— parameter, 

r|j = correlation coefficient for i— and j— parameters 



Assume that the embankment of consideration is not "zoned"; that is, it is of a 
homogeneous nature. 



Fellenius' equation for the factor of safety (F) for soils may be written as 

- cL + tan <j) £ (y A| cos 0[ - U] A£|) 
Y Z|Aj sin 0| 

where c = cohesion of soil, 

<j) = angle of internal friction, 

L = total arc length of slip circle, 

Y = density of soil, 

Uj = pore pressure, i— slice, 

Aj = area, i— slice, 

0j = angle of tangent to arc, it-^ slice, 

AA| = arc length, i— slice, 

and £ = summation over the "i" slices, i = 1, n. 

TABLE 1. - Basic statistics for soil parameters 



(3) 



Slope stability 
parameter 



Mean 



C v , pet 



Slope stability 
parameter 



Mean 



C v , pet 



CDA SITE (74 SAMPLES) 



SW SITE (130 SAMPLES) 



* ■ 

c 

Y 

F-Bishop..., 
F-Fellenius, 



-deg 
.psi 
.pcf 



36.74 

3.52 

114.00 

1.54 

1.43 



2.18 

2.94 

6.06 

.41 

.40 



5.9 
83.5 

5.3 
26.6 
28.0 



* 

c 

Y 

F-Bishop. .. 
F-Fellenius , 



.deg 
.psi 
.pcf 



39.13 

4.32 

106.85 

2.07 

1.95 



4.14 

4.14 

5.65 

.27 

.24 



10.6 
95.8 
5.3 
13.0 
12.4 



<}> = angle of internal friction. 

c = cohesion. 

Y = soil density. 

F = factor of safety. 



Mean = sample average value. 

S = sample standard deviation. 

Cw = coefficient of variation = 



100-S 

■ 

mean 



See figure 1 for the geometry of Fellenius' method. 

Applying the propagation of error formula to equation 3 yields 



,2 2 



s F = *> s^ + F c s c + F y s y + I F U| s u 



2 r c ,y F c F Y s c s Y + 



. + 2r 



u n-1 



+ 2r c,<|> F c F <|> s c s <j> 



"n-r u n &u n-r u n. 



(4) 



The required partial derivatives are 



u ? 



and 



Y E A| sin G| ' 

sec 2 <{> Z (y A| cos 0|- U| &l\) 
~~y £ A| sin 

-tan <}> A£j 

Y E A| sin Oj ' 

-cL + tan <f» Zu| Mj 



Y 2 I A| sin 0, 



(5) 
(6) 
(7) 
(8) 



Of particular interest is the selection 
of Fellenius' equation rather than that 
of Bishop. Fellenius 1 equation gives a 
"closed solution" for the factor of safe- 
ty value, while Bishop's equation is not 
nearly so convenient, with an iterative 
process being required for solution. Al- 
so, many practioners and soil mechanics 
text authors still seem to prefer Felle- 
nius' formulation. Later in this report, 
the propagation of error methodology will 
be applied to the collected data sets. 

A proper measure of the uncertainty of 
the factor of safety involves more than 



simply computing its standard deviation. 
Pore pressure uncertainty is a very im- 
portant topic in itself (3, 1J), 14 ) and 
is currently considered the weak link in 
error analysis of the factor of safety 
value. Spatial variability could be as- 
sessed through three components: (1) the 
natural heterogeneity of the soil, 
(2) measurement error, and (3) limited 
information about subsurface conditions. 
Anderson (2^) discusses the merits of con- 
sidering model error when assessing the 
variability of the factor of safety. 



DISTRIBUTION PROPERTIES 



Data were collected at two sites — 
a silver-lead-zinc mine in the Coeur 
d'Alene mining district of Idaho (CDA 
data), and a Southwest U.S. copper mine 
(SW data). The appendix describes the 
field collection of the data. Table 1 
enumerates basic statistics from these 
two sites; effective stress is used 
throughout. 

Note that a rather large number of sam- 
ples were obtained at each site, giving a 



significant population size for consider- 
ation. The variability in the internal 
angle of friction (<))), cohesion (c), and 
soil density (y) is consistent with the 
results of Lee and Singh's (11) earlier 
works. In fact, <(> has less variation 
than anticipated, although Singh's work 
focused on variability between laborato- 
ries rather than on within-laboratory 
variability. Note the close relationship 
between the values of Bishop's factor of 
safety and that of Fellenius. Since the 



propagation of error work uses Fellenius' 
factor of safety, we will only use Felle- 
nius' numbers henceforth. 

To better visualize the data, histo- 
grams of the data are shown in figures 3 
through 6. In figure 3, histogram of the 
factor of safety, note the wide variabil- 
ity in the CDA data. Over 10 pet of the 
data lies to the left of 1; thus the 
probability of failure is predicted to 
be quite high. However, there are two 
points to keep in mind: 



paper considers the normal, log-normal, 
and Weibull distributions. Table 2 sum- 
marizes curve-fitting these functions to 
Fellenius' factor of safety values. 



Two interesting points 
from table 2: 



may be drawn 



1 . The logarithmic transformation does 
not improve fitting the PDF's. This is 
reasonable, for the log-normal transfor- 
mation works best for data that are ini- 
tially skewed to the left. 



1. In this case, the material is con- 
tained behind a berm of borrow material; 
thus the factor of safety values are sim- 
ulated, not actual values. 

2. This wide variability gives credi- 
bility to the variance reduction concept, 
which is intrinsic to the probabilistic 
work of Vanmarcke and Anderson (2^, 16 ) . 
Thus, variance reduction, although a con- 
troversial concept as a "pragmatic value" 
at this time, is conceptually acceptable 
and at least partially verified as to 
need by this distribution. 

Certainly the histogram for the factor 
of safety (fig. 3) demonstrates a strong 
central tendency in both cases; the next 
logical question is whether a conven- 
tional mathematical PDF "fits" the data 
properly or not. There are many candi- 
date functions for consideration; this 



2. The Weibull PDF does not improve on 
the curve fits for the normal PDF. Since 
the Weibull is more "obscure" (for exam- 
ple, parameters are not easily under- 
stood, and the curve-fitting is appreci- 
ably more difficult) , there seems to be 
no reason to use it in preference to the 
normal PDF. 

It is true that there are other candi- 
date distributions — the beta, gamma, 
Poisson, et al. — that could have been 
considered. In particular, the geotech- 
nical community has shown some preference 
for the beta PDF. Upon investigation of 
the properties of the Weibull and beta 
PDF's, it is found that both are versa- 
tile functions that can fit a variety of 
situations in a very similar manner. Our 
choice is to investigate just the Weibull 
PDF in this report. It is felt that this 
investigation is sufficient and the 



TABLE 2. - Three model curve fits to Fellenius' factor of safety 



Probability 

density 
functions 1 


Index of 
determination 2 


X 2 values 3 


Probability 

density 
functions 1 


Index of 
determination 2 


X 2 values 3 


CDA SITE 


SW SITE 


Log normal. . . 


0.62 
.59 
.62 


4 18.41 
NA 
NA 


Log normal . . . 


0.96 
.94 
.96 


5 6.13 

NA 
NA 



NA Not available. 

1 A11 curve fitting done using Gauss' nonlinear iterative technique (13). 



Measures how well the data agree with curve-fit function. Reduces to the correla- 

used for comparison is 9.49 for these 



tion coefficient in the linear case (13) . 
3 Goodness-of-fit test; the critical value 



cases. 

4 



Reject. 
5 Accept. 



20 



> 

o 

Z 40 

M 

O 



3d 



Coeur d' Alene 




20 



■ : 



Southwest 



F = 1.95 
S c =0.24 




0.6 1.0 1.4 1.8 2.2 2.6 3.0 

F (FELLENIUS) 

FIGURE 3. - Factor of safety histograms. 





I 


I I 

^^r\ Coeur 


flT 


Alene 




10 








c =3.53 
S c =2.94 








H 


i Vr 




I 





40 

> 
O 

z 

M 

O 30 

LU 
X 



20 



10 




COHESION, psi 

FIGURE 5. - Cohesion histograms. 



30 



20 



10 



40 



30 



20 



10 




25 30 35 40 45 50 
PHI ANGLE, deg 

FIGURE 4. - Internal friction angle histograms. 



20 



uj 

° 30 



Coeur d' Alene 




Southwest 




FIGURE 6. - Soil density histograms. 



normal PDF is as good a choice as can be 
made for these two examples. It is true 
that the normal distribution's curve fit 
to the CDA is not outstanding as indi- 
cated by the chi-square measure. The 
data are simply not conducive to a good 
curve fit, regardless of what function 
one might try. 

Table 3 enumerates pertinent statistics 
and curve-fit parameters for internal 
angle of friction, cohesion, and density. 

In view of the preceding discussion, 
and since the remaining PDF's are of 
lesser interest to us, only the normal 
curve will be used to fit these histo- 
grams. The internal angle of friction 
distributions (fig. 4), although again 
demonstrating central tendency, are each 
skewed, both to the right. The index of 
determination for both fits is satisfac- 
tory, with a somewhat better fit for the 
SW data. Note that the fitted parameters 
vary somewhat from the sample means and 
standard deviations; the degree of vari- 
ability is a function of the goodness of 
fit. 



It is not surprising that the cohesion 
value (fig. 5) has the largest variabil- 
ity, for this is apparently inherent in 
the cohesion parameter ( 11 ) . Thus the 
normal curve approximations to the cohe- 
sion histograms are not particularly im- 
pressive, as indicated by the relatively 
low indices of determination. Here the 
histograms would indicate a slight skew- 
ness to the left. 

Finally, consider the histogram (fig. 
6) for the soil density. Again, curve 
fitting these curves is of somewhat nebu- 
lous value; for example, a uniform dis- 
tribution may be a better candidate for 
the SW data. But to be consistent, the 
normal curve approximation was used; the 
resulting indices of dispersion reflect 
the degree of disagreement between the 
data and fitted function. 

To summarize, central tendency is ex- 
hibited by all of the histograms (and 
corresponding PDF's) considered. The 
normal curve seems to be an acceptable 
candidate model. For consistency's sake, 
the normal curve was then used for all 



TABLE 3. - Normal curve-fit parameters for <j> , c, 
y, and F 



Normal curve-fit 



parameter 



Area 



Mean 



Index of 
determination 2 



CDA SITE 



♦ 

c 

Y 

F-Fellenius 



.deg.. 
.psi. . 
.pcf. . 



118.78 

115.22 

147.38 

14.14 




0.82 
.79 
.62 
.62 



SW SITE 



* : 

c 

Y 

F-Fellenius, 



,deg.. 
.psi. . 
.pcf. . 



291.09 

296.44 

441.30 

17.72 




.91 
.85 
.88 
.96 



1 Equation for normal PDF used: 

- (x - mean) 2 /2 (std. dev.) 2 



y = 



(area) 



/2rr (std. dev.) 
where y = dependent variable (histogram value) , 
x = independent variable (F, <)) , c, y)> 
2 A measure of goodness of fit for nonlinear functions; 
see reference 13 for details. 



histogram curve fitting. Also, the se- 
verity of concern decreases considerably 
as one moves from the factor of safe- 
ty to the supporting data sets. Thus, 
for probabilistic work, in finding the 



probability of failure and in setting 
confidence intervals on the estimated 
mean factor of safety value, these two 
examples fortify use of the normal proba- 
bility density function. 



PROPAGATION OF ERROR APPLIED TO THE DATA 



As stated previously, it is desirable 
to take only a few field samples and use 
the propagation of error technique (6) to 
estimate the variance of the factor of 
safety. However, since we have complete 
sets of data available, we naturally used 
all these data for comparative slope sta- 
bility work herein. (See appendix for 
the data description.) Table 4 shows the 
coefficient of variation for Fellenius' 
factor of safety value with assumed pore 
pressure coefficient of variation values 
of 0, 10, and 20 pet. These values are 
compared to the sample coefficient of 
variation value. In the case of the SW 
embankment , the agreement between the 
propagation values and that of the sample 
data is quite good. The CDA data do not 
agree as well, but the divergence would 
seem acceptable. Note that the pairwise 
correlations between the soil parameters 
(for example, "<j>" and "c") may or may not 
be included in the computations, depend- 
ing on the user's preference. We chose 
to use these correlation coefficients in 
our computations. Table 5 enumerates the 



pairwise correlation coefficients used in 
calculating table 4. 

TABLE 4. - Comparison of coefficient 
of variation estimates for Felle- 
nius' factor of safety 



Coefficient of variation 



pet 1 

10 pet 1 

20 pet 1 

Actual sample values 2 




1 The entries are the propagation of er- 
ror computed values for the specified 
pure pressure. 

2 The entries are the comparative values 
obtained from the available sample data — 
see table 1. 

TABLE 5. - Correlation coefficients 



Correlation coefficient 
r c,4> 

r c,Y 

r <J>,Y 




CONFIDENCE INTERVAL FOR THE FACTOR OF SAFETY 



There is one basic statistical approach 
that can be easily applied to the factor 
of safety computation which provides a 
simplistic marriage between the world of 
probability and the presently used deter- 
ministic computation — putting a confi- 
dence limit about the factor of safe- 
ty value. A brief review of statistical 
principles would seem in order. Suppose 
one is concerned with a variable whose 
PDF is not necessarily normally distri- 
buted, but for which the population mean 
and standard deviation exist. Next, a 
sample size "n" is chosen. By some ran- 
dom process, "n" samples are selected 
from the original population and a sample 
mean (x) is computed. This process is 
then repeated until a population of 



sample means (all of which are of the 
preselected sample size "n") exists. The 
Central Limit Theory of Statistics states 
that the PDF of mean values will be nor- 
mally distributed provided "n" is suffi- 
ciently large. Furthermore, the popula- 
tion mean of the new distribution — the 
distribution of sample means — is the same 
as the population mean of the original 
PDF, but the standard deviation of the 
new distribution equals the original 
PDF's standard deviation divided by the 
square root of "n." When the Central 
Limit Theorem is actually applied to a 
data set, only one sample of size "n" is 
taken from which the sample mean and 
standard deviation are computed. 



10 



This powerful theorem can be applied to 
the distribution of factor of safety val- 
ues. The key of the theorem is, of 
course, how many samples are required for 
it to be valid. The answer to this query 
is certainly not simple; if the original 
distribution is very similar to the nor- 
mal curve, then small sample sizes suf- 
fice. For symmetrical distributions (the 
preceding work and that of Baecher and 
Marr (_3) substantiate that one may assume 
symmetry) , a sample size of eight or 
greater would seem appropriate. Thus the 
computational procedure would be as 
follows: 



1. Collect a representative set of 
soil properties; a minimum of eight sets 
is recommended. Compute a corresponding 
set of factor of safety values. 

2. Compute the sample mean (F) and 
standard deviation (s F ) for these factor 
of safety values. 

3. Apply the Central Limit Theorem by 
forming a 95-pct confidence interval for 
the true but unknown population mean fac- 
tor of safety value (up). The following 
computation is requisite: 



where 



F ± to. 975 ( n ~l) * s f/ ^i = 95-pct confidence interval, 
n = sample size, 



and tg. 975 (n-1) = "t" distribution value, which depends on sample size 

and the level of confidence. 



- 1 



There is no set rule that mandates a 95- 
pct confidence interval; this is a con- 
ventional and conservative choice. 

Let us investigate what it meant by a 
confidence interval. For example, a 95- 
pct confidence interval implies that if 
one were to form 100 such intervals , 
95 of these would contain the true (but 
unknown) population parameter. In prac- 
tice, one computes only one such interval 
and relies on statistical theory to pro- 
vide the statement of confidence or 
assurance. 

A simulation may prove illustrative. 
The authors selected, via random sam- 
pling, 16 sample factor of safety values 
from each of the previously discussed 
data populations. It was assumed that 
the computed sample mean value was a best 
approximation to the true factor of safe- 
ty value. Then confidence intervals for 
subsamples of size 4 were formed, then of 
size 8, and finally of size 16. These 



confidence intervals are shown in figures 
7 and 8 for the two data populations of 
interest. Note that in all but one case 
the 95-pct confidence intervals did con- 
tain the overall sample mean. Also, note 
that the intervals tend to lessen in 
length as the sample size increases. In 
figure 7 — the CDA data — samples of size 4 
include factor of safety values less than 
1 in three of the four cases. Also, one 
of the two samples of size 8 extends be- 
low a factor of safety value of 1. This 
is, of course, an indicator of concern 
for the embankment designer. 

Again, the preceding simulation is tu- 
torial, for in practice one would obtain 
only one confidence interval and use it 
to make a statement about the factor of 
safety. Furthermore, an example is, at 
best, illustrative and certainly does 
not replace theoretical considerations. 
Ideally, the interval would contain no 
factor of safety values below the criti- 
cal value of 1. 



GEOTECHNICAL INNOVATION AND PROBABILISTIC MODELING 



There is a new approach regarding 
the "best" model for the factor of 
safety calculation. The traditional 



two-dimensional slip circle of Fellenius 
and Bishop is being challenged. In par- 
ticular, a three-dimensional cylinder has 



11 



3.0 



2.6 



2.2 



n = 4 



>- 
LU 



< 1.8 — 
CO 



O 1.4 = 



O 

< 



1.0 



.6 (— 



n = 8 



n = 16 



F F = 1.43 



, F I 



Accep 
Reject F 



FIGURE 7. - Ninety-five percent confidence 
interval-factor of safety, CDA Mine— with vary- 
ing sample size. 

been postulated by Vanmarcke and others 
(—> 16) • Theoretical development reduces 
the cylindrical model effectively to that 
of Bishop (5, 9_) , but with end-effect 
forces considered. 

A most important concept in the geo- 
technical works of Vanmarcke (16) and 
Anderson (2^) is variance reduction. This 
rather complex topic is explained in 
depth in the two aforementioned refer- 
ences; the following is a heuristic over- 
view. Rather than being interested in 
the usual statistical value of the vari- 
ance of the strength parameter, the geo- 
technical engineer is concerned when a 
succession of weak strength values oc- 
curs. In such a case, the possibility 
of failure is greatest. If one were to 
envision a moving average curve being fit 
to a spatial succession of strength val- 
ues, the variability from the moving 



^ .0 


n=4 






2.2 


__ 




r n = 8 


















n= 16 


>- 




















UJ 








i > 








F F =1.95 






1 i 




— 1 1 






U. 


ii < 




i > 




' 


< 1.8 


















— 


CO 




















LL 












-*- 




o 














DC 




- 1 - 






O 1.4 






— 


h- 








O 








< 








LL 






Accept F | 








1.0 






Reject F I 



FIGURE 8. - Ninety-five percent confidence 
interval— factor of safety, SW Mine— with varying 
sample size. 

averages is representative of the desired 
reduced variance (fig. 9). A scaling 
factor, variance reduction, is used to 
reduce the statistical variance value to 
the desired variance value. The actual 
computation of the scaling factor is not 
as simple as described herein. Involved 
is a plot of the autocorrection function 
for the values of concern. Next, a curve 
is fit to the autocorrelation function, 
and said function is included in an inte- 
gration that computes the desired reduced 
variance value. 

Two major problems in the application 
of the probabilistic model were found 
during a recent field test under a Bureau 
of Mines contract. One concerns the ef- 
fects of variance reduction on the prob- 
ability of failure, and the other is the 
high cost of obtaining strength data 
using a penetrometer. 

The variance reduction value proved to 
be quite severe, effectively reducing the 
factor of safety PDF to a single spike. 
The dilemma is that one has gone through 
the complex mechanism of probabilistic 
slope stability and has only obtained a 
univalued answer, as in the deterministic 



12 



Q 




LU 




O 




< 


CO 

1 


LU 


T 


> 


\- 


< 


(D 


> 


Z 


_l 


LU 


-1 


DC 


< 


H 


1- 


CO 


< 




0- 




CO 





KEY 



Sp=Point standard deviation of data 
S r =rSp=Reduced standard deviation 

s r §i 



r=Variance reduction factor 
S=Mean strength value 



t 




V^ 




FIGURE 9. 



DISTANCE ALONG EMBANKMENT CENTERLINE 

Variance reduction applied to spatially oriented shear strength values. 



approach. Only replicated fieldwork will 
verify whether or not this is the general 
case. 

To accommodate the computations for 
variance reduction, a sequence of closely 
spaced strength values must be obtained 
in all three dimensions of the dam or 



embankment. Cone penetrometer soundings 
are required to gather the necessary in- 
formation. This adds greatly to the cost 
of obtaining the factor of safety. The 
obvious question to be answered is wheth- 
er the benefits gained from a probabilis- 
tic analysis justify the increased cost. 



CONCLUSIONS 



A large sample of direct shear tests 
was taken at two waste embankment sites. 
Of the statistical model tested, the nor- 
mal probability density function best fit 
these data. This conclusion is site spe- 
cific and should not be imprudently ex- 
trapolated. The authors are aware that a 
wealth of data is now available to the 
mining industry, since penetrometers of 
various kinds are now being used more 
frequently. Thus, detailed investigation 
of the variation of strength with depth 
can now be routinely incorporated to make 
computations more meaningful. In fact, 
the Bureau has contracted for soil param- 
eter collecting using cone data ( 3) . The 
Bishop code with the propagation of error 



and probability of failure calculations 
is available from the Bureau for inter- 
ested users. 

A suggested first step towards intro- 
ducing useful probabilistic concepts into 
the factor of safety computation is to 
compute a confidence interval about the 
average factor of safety value , replacing 
current usage of a conservative determin- 
istic factor of safety value. It would 
seem most advantageous not only to know 
the factor of safety value but to have a 
sense of the error in that value and an 
indication of how good or reliable the 
factor of safety might be. 



13 



REFERENCES 



1. Alonso, E. E. Risk Analysis of 
Slopes and Its Application to Slopes in 
Canadian Sensitive Clays. Geotechnique, 
v. 26, No. 3, 1976, pp. 453-472. 

2. Anderson, L. , D. Bowles, R. Can — 
field, and K. Sharp. Probabilistic Mod- 
eling of Tailings Embankment Designs. 
Volume 1. Model Development and Verifi- 
cation (contract J0295029) . BuMines OFR 
16KD-82, 1982, 233 pp.; NTIS PB 83- 
122598. 

3. Baecher, Marr, & Associates. Cri- 
tical Parameters for Tailings Embank- 
ments . Ongoing BuMines contract 
JO215018; for information contact D. R. 
Tesarik, Spokane Research Center, Bureau 
of Mines, Spokane, WA. 

4. Bailey, W. A. Stability Analysis 
by Limiting Equilibrium. CE Thesis, 
Mass. Inst. Technol. , Cambridge, MA, 
1966, 63 pp. 

5. Bishop, J., and N. Morgenstern. 
Stability Coefficients for Earth Slopes. 
Geotechnique, v. 10, No. 4, 1960, pp. 

129-150. 

6. Deming, W. E. Statistical Analysis 
of Data. Dover Publishing Co. , New York, 
1964, pp. 37-48. 

7. Harr, M. E. Mechanics of Particu- 
late Media. McGraw-Hill Book Co., Inc., 
New York, 1977, pp. 427-442. 



Denver, CO, 1978, pp. 1-16; available for 
consultation at Spokane Research Center, 
Bureau of Mines, Spokane, WA. 

10. Lambe, T. W. , W. Marr, and F. Sil- 
va. Safety of a Constructed Facility: 
Geotechnical Aspects. J. Geotech. Eng. 
Div., ASCE, v. 107, No. GT3 , Mar. 1981, 
pp. 339-352. 

11. Lee, K. L. , and A. Singh. Report 
of the Direct Shear Comparative Study. 
Soil Mechanics Group, Los Angeles Sec- 
tion, ASCE, Nov. 1968, pp. 1-38. 

12. Lumb, P. Probability of Failure 
in Earthworks. Proc. 2d Southeast Asian 
Conf. Soil Eng., Singapore, Sept. 1970, 
pp. 139-148; available from authors of 
this report. 

13. McWilliams, P., and D. Tesarik. 
Multivariate Analysis Techniques With 
Application in Mining. BuMines IC 8782, 
1978, pp. 22-27. 

14. Mittal, H. K. , and N. Morgenstern. 
Seepage Control in Tailings Dams. Can. 
Geotech. J., v. 13, 1976, pp. 277-293. 

15. Sharp, K. , L. Anderson, D. Bowles, 
and R. Canfield. A Model for Assessing 
Slope Reliability. 60th Ann. Meeting, 
Transportation Research Board, Washing- 
ton, DC, Jan. 1981, 40 pp.; available 
from authors, Chem. Eng. Dept. , Utah 
State University, Logan, UT. 



8. Hoel, P. Introduction to Statis- 
tics. John Wiley and Sons, Inc., New 
York, 3d ed. , 1962, pp. 139-145. 

9. Jubenville, D. Limit Equilibrium 
Slope Analysis and Computer Software. 



16. Vanmarcke, E. Reliability of 
Earth Slopes. J. Geotech. Eng. Div., 
ASCE, v. GT11, Nov. 1977, pp. 1247-1263. 



14 



APPENDIX. —DATA COLLECTION, SLOPE STABILITY, AND LABORATORY TESTING 



DATA COLLECTION--CDA 

A detailed investigation of the im- 
poundment facility was not undertaken, 
since the scope of this project was to 
determine strength variability in the 
beach material and to model an embankment 
consisting solely of this material. 

The embankment was constructed by the 
upstream method using a starter dike of 
borrow material. The dike is built 
against a steep side of a valley with an 
overall downstream slope of 2:1. The im- 
poundment area covers approximately 7 
acres. Tailings were deposited from 
spigot lines extended from the crest of 
the embankment. They contain from 15 to 
50 pet material passing the No. 200 U.S. 
Standard Sieve. In general, the coarser 
material settled out close to the crest, 
but a layering effect became evident 
while sampling. Fluctuating pond size 
and different spigot locations could have 
caused this phenomenon. 



for the computer model. These were se- 
lected to evaluate a potentially unsafe 
condition (that is, P (failure) > 0) and 
in no way reflect the actual conditions 
of the embankment from which the soil was 
extracted. The location of the phreatic 
surface, based on the 10 pet freeboard 
headwater, was determined by the finite- 
element method (4). 2 No tail water was 
assumed in the model. The material in 
the embankment was assumed to be homoge- 
neous to the extent that no layers were 
coded into the model. The code was exe- 
cuted using 74 sets of strength parame- 
ters (c, <j) , y,) in order to calculate the 
coefficent of variation of the factor of 
safety and compare it to the value ob- 
tained by using the propagation of error 
formula. The value for density that was 
used in each run was an average of the 
densities of the samples used to conduct 
the direct shear test for a corresponding 
c, <J>. 

DATA COLLECTION— SW 



Data were taken along the perimeter of 
the embankment 15 ft from the crest at 
intervals of 150 ft. At each data loca- 
tion, four thin-wall, 3-in-diam Shelby 1 
tube samples were taken at the corners of 
an imaginary square measuring 2 ft on 
each side. Before inserting the Shelby 
tubes by hand, the tailings were in- 
spected for disturbance and cracking. 
If either of these conditions existed, 
the cluster of four tubes was displaced 
slightly to avoid the irregularity or 
cracks. When the tubes were extracted, 
the ends were capped and sealed, and the 
tubes were placed in a foam-lined con- 
tainer for transportation by truck to the 
laboratory. Care was taken that minimum 
sample disturbance occurred. 

STABILITY ANALYSIS— CDA 

A slope of 2 to 1 and a phreatic sur- 
face having 10 pet freeboard were chosen 

1 Reference to specific trade names is 
made for identification only and does not 
imply endorsement by the Bureau of Mines. 



As with the CDA embankment, an exten- 
sive field investigation was not under- 
taken. A brief, general description will 
again be presented. 

The SW tailings embankment has been in- 
active for years. It was constructed 
from copper tailings , using the upstream 
spigoting method. The slurry was about 
45 pet tailings by weight; the tailings 
grind was 40 pet passing the No. 200 
Sieve and 75 pet passing the No. 65 
Sieve. The embankment is bounded on one 
side by another tailings embankment. The 
tailings pond covers approximately 300 
acres and averages 300 ft high. The 
overall slope is approximately 2 to 1. 

The data for the SW embankment were 
also collected using thin-wall Shelby 
tubes. The embankment had from 6 in to 
several feet of overburden placed on 
top of the tailings for dust control 

^Underlined numbers in parentheses re- 
fer to items in the list of references 
preceding the appendix. 



15 



purposes. The top 3 to 5 ft of tailings 
was compacted from equipment placing the 
overburden; in some cases, desiccation 
was apparent. An attempt was made to in- 
sert the Shelby tubes using a jack, with 
resistance provided by a truck. This 
caused too much sample disturbance so a 
front-end loader was employed to scrape 
off the overburden and push the Shelby 
tubes into the embankment. (The tubes 
inserted by the jacks were not included 
in the data analysis.) 



SAMPLE TESTING 

Standard direct shear tests were per- 
formed on a series of samples extracted 
from the Shelby tubes with a circular 
trimmer ring. Owing to the time needed 
to test all the soil samples, some corro- 
sion took place inside the Shelby tubes. 
These samples were sawed in half to re- 
duce sample disturbance when the soil was 
extracted from the tube into the trimmer 
ring. 



The tubes were extracted by hand, 
sealed, and packed into foam-lined boxes 
for minimal disturbance. It was neces- 
sary to lay the tubes in a horizontal po- 
sition for shipping. 

The data station pattern is shown in 
figure A-l. This pattern was chosen so 
that correlations might be studied based 
on distance from the crest and spacing 
distance between data points. 

Unlike the CDA embankment, the computer 
model was set up to reflect the geometry 
and phreatic surface location of the ac- 
tual embankment. The cross section that 
was used is shown in figure A-2. The ac- 
tual embankment had a starter dike that 
was not included in the analysis. This 
exclusion could produce lower factors of 
safety than actually exist. All 130 
triplets (c, <f> , y,) were run through the 
computer code to obtain the 130 values 
of the factor of safety necessary to 
calculate the PDF and coefficient of 
variation. 



Each sample was consolidated before 
shearing by applying normal load to allow 
for drainage. Initial displacement mea- 
surements from consolidation, along with 
direct shear test data, are given in ta- 
bles A-l and A-2. At a minimum, normal 
stresses of 25 psi, 50 psi, and 100 psi 
were used. For the CDA data, an addi- 
tional point of 75 psi was used to deter- 
mine each <f> , c combination. Owing to the 
layering effects of each embankment , it 
was necessary to repeat various normal 
loads to ensure that enough data were 
available for a good least squares curve 
fit for <|> and c. Average shearing rates 
for the tests were 0.305 mm/sec for 
the 25-psi normal load, 0.275 mm/sec for 
50 psi and 75 psi, and 0.25 mm/sec for 
100 psi. The slow rate was used to pre- 
vent pore pressure buildup and ensure 
drainage. 

Cumulative grain-size distribution 
tests were run for 14 tubes from the CDA 
data. At least one tube was tested from 
each data location in an attempt to 



• • 



• • • • • 

• • • • • 



—I k-25' 



324' 



Embankment! crest 



FIGURE A-l. - SW data station pattern 



16 



represent the range of data collected. A 
range of distributions is shown in figure 
A-3. 

COMPUTER PROGRAM FOR PROPAGATION 
OF ERROR 



The computer program used to 
the coefficient of variation of 
tor of safety is a modified vers 
program written by Bailey (4). 
gram uses Bishop's Simplified 
Slices to determine the minimum 
safety for a given embankment 
The failure surface is assumed 
arc of a circle. 



calculate 
the fac- 
ion of a 
The pro- 
Method of 
factor of 
geometry, 
to be an 



The program divides the slope cross 
section into vertical slices and evalu- 
ates moments about the circle center 
using the force vectors at the base of 
each slice. The horizontal side forces 
and vertical shear forces on each slice 
are not used in the calculations. The 
number of slices is input by the user 
but may be altered slightly by the 
program so that slice boundaries coin- 
cide with selected points on the 
embankment . 



500 



The slice boundaries are determined be- 
fore any trial circles are analyzed, so 
the number of slices in each sliding mass 
varies with the radius of the trial cir- 
cle. To determine a minimum factor of 
safety, the program evaluates 1,331 trial 
circles. The center of each circle is a 
point on an imaginary square grid placed 
above the slope of the embankment. At 
each point on the control grid, the pro- 
gram computes a minimum radius; that is, 
a radius that will just touch the slope 
and a maximum radius based on the geome- 
try of the slope profile. A series of 
factors of safety is computed, starting 
with a radius slightly smaller than the 
maximum radius. Each successive radius 
is reduced by approximately one-eleventh 
of the difference between the minimum and 
maximum radii. 

Coefficients for evaluation of equation 
4 are required for input in addition to 
embankment geometry, phreatic surface in- 
formation, and soil parameters. The pro- 
gram outputs the coefficient of vari- 
ation and standard deviation for the min- 
imum factor of safety, the probability of 
failure (assuming normal statistics), and 




200 



300 400 500 600 700 

HORIZONTAL DISTANCE, ft 
FIGURE A-2. - Idealized profile-SW embankment. 



800 



900 1,000 



17 



100 
90 
80 



? 70 



o 
a 



60 



a» so 
o 

S 40 



30 
20 
10 



U.S. Standard Sieve sizes 

30 40 50 70 80 100 140 200 325 


400 




\ 




















































/ / / 


N 














































\ 
















































Y 


/ 




U 




' / 












































// 







9, 














































// 






// 


t£ 




































\ 




h 

J 


>; 






& 








































! / 
i 


i 




// 


t 


'/// 














































ti 






' 
















































V 




/ 





























































5 4 3 



198765 4 



.01987 6 5 4 



GRAIN SIZE, mm 

FIGURE A-3. - Range of grain-size curves for CDA data. 





10 

20 

30 

40 

50 

60 

70 

80 

90 

100 



0) 
(0 

« 
o 
o 

o 
a 

CO 
O 



.001 



the contribution by term (equation 4) to 
the standard deviation of the factor of 
safety. 

The pore pressure in the computer pro- 
gram is calculated at the base of each 
slice, based on static head. Similarly, 
the contribution to the error term by 
pore pressure is on a slice-by-slice 
basis. Since the user inputs the coef- 
ficients of variation, it is convenient 



to calculate both the variance term 
and the covariance terms for pore pres- 
sure. In our calculations, it was as- 
sumed that the correlations between pore 
pressures and the strength parameters 
= 0, and that the correlations between 
pore pressures for any two slices = 1. 
The covariance terms for the strength 
parameters are included; that is, r c x 

r c,Y, and r <J>,Y. 



18 





c 
o 

■H i-l 
CO CO 

<D O. 

XI 

o 
u 


VO 
CM 

CO 


o 
-3- 

CO 


vo 

CM 
00 


m 

CM 


CD 
O 


—4 


O 

o 


CM 

O 

-3- 


O 

o 


CO 


vO 
-3 




cfl O » 
C -H OJ 
l-i -U iH M 
« U bOll 
■U f-l C T3 
C 1J tfl 
l-l K-l 


CD 
VD 

•* 

co 


m 
m 

CO 


cd 

rs 

rs 

CO 


oo 

CO 


00 
CO 

in 

CO 


VO 
O 

in 

CO 


CD 
vO 

l-~ 
CO 


CM 
CM 

m 

CO 


in 
o 

is 
CO 


Is 
CD 

in 

CO 


00 
CM 

is 
CO 




(0 K-l 
3 O 
•H >-, 

d u j_> 

0)0 0) 
H 4J K-l 

■H O to 

HI U li) 
tn K-l 


is 
ps 

CO 


ps 
is 

CO 


vO 
CM 

#— i 


00 
-3- 


o 
o 


CM 
CM 


CO 
CD 
vO 


-3- 
~3- 


■3- 
00 

vo 


o 

CD 


CO 
CM 
CD 




>s 

4-1 
4J T-l K-4 
CU to CJ 

3 c a 

CU 
TJ 


IS CD CM in 

rs —i o vo 

O — i O -* 
-I tN CN N 


CO ~H vD 
-3- CD —I 

o o m 

CM CM -H 


rs vo is 

— < CM vD 

CM CO CO 
~H CM — 1 


•-< CM O 
CO O^ G\ 

cd ^ in 

O CM — i 


— I O vO 00 
00 CM cm in 

CM -3- ^ CO 


-3- -h cm m 
o in oo co 

CD CO -3- CO 


•—1 CD CO ^\ 
00 O ~h vO 

CM CD <3 00 

— 1 O — 1 -< 


HPlOlO 
CM CD co r^ 

•3 n tn-j 
O O O O 


co m is 

— i -3- is 

CO CO o 
—I —< CM 


oo in is 
-3- -h is 

—I CM CD 
CM CM —I 


00 CM -H O 

in is m oo 
is is in co 

—I —I —I CM 




CO 
^ CO i-l 

CO cu to 
cu i-i a 

CO 


Cft N N O 
i—l CD CO CO 

O m o cm 

CM CO <P 1 — 


in s co 
in cm in 

O CD CO 
cm co rs 


m co CD 

st rs CD 

CD O Is 
rt -3- p^ 


in ^ ~h 
vO 00 O 

— 1 -4 O 

CM -3 00 


CM O v£> -3- 

co m mo cd 

CD sD CO CM 


CD CM CM CO 

r- o r~ co 

00 r^ -3- i-i 

hio in n 


CD -3- CM 00 

i^ m co in 

CO 1^ |v vO 

hco m s 


O O O rv 
CM 00 O 00 

CM Pv O <f 

cm ci <■ rv 


is CO is 

—1-3-00 

00 Is <3- 
^h CO IS 


is O Is 
-H IS vO 

00 VD CM 
-H CO IS 


CO CM VO Is 
CD 00 -3- 00 

is CD CD -3- 

-h co m is 


to 
4-1 


H 1 

to tO « 
•H (J C 4J 
4-> 3 o CJ 
•H 4-1 i-l a. 
C CO 4J 
H CO 


in o O rs 
— i O 00 CM 

CO O CO vo 
rs o co cd 


c\ — I <■ 

N n rs 

H(MN 
CD CO vO 


N CON 
rs 00 vO 

CM -H CD 

IDO) CO 


CO CD CD 
O CM CM 

CM -H \D 
vO 00 VD 


O CO 00 00 
CO •* CD CM 

O mO r^ o 
CD r*. T^ CD 


cd oo o in 
O ~h o m 

CD r^ in -3- 
co co n oo 


o m vo o 
vo r^ cm >3- 

m -* o o 

N \0 N CO 


P*- CO CO CD 
m CM VO CO 

^\ &\ ~H vO 

•* in in -3 


CD 00 O 

iH O O 

o in o 
CD 00 o 


— i CD O 
m cm o 

CO CM O 
00 CD O 


O vD in CM 
CM CM 00 vO 

CM CD CM CO 
CD Is 00 CD 


Ss 
U 

o 

4-1 

CO 

IJ 


.O 
« 

< 

a 
o 

i 


1 

■H >v 
HT3 4J 
O CU >si-4. K-4 
CO 4-1 kl CO U 

c to t3 c a 

O TJ HI 
O TJ 


h vo vO i£ 
<T CO VO CD 

vo *-i st cd 
cd o o o 


vD vO O 

CO — I — I 

co st <r 
o o o 


00 CD ^O 
v£) CD CO 

CD O O 


00 CM CM 

-H O — 1 

\Oh. \D 

CD O O 

■ — i i— * 


in .-4 r~. -3- 
vO r^ r^. cd 

00 00 vO 00 
00 CD CD CD 


CO CM CO 00 
-3- m CO CM 

co r^ co cm 

CD CD O O 


oo in in o 
-3- o ~* o 

vo cd i— i r*» 

CD CD O O 


CM 00 P^ CD 

n pv in m 

CO -3- ~h CD 
CD CD CD CD 


O -h O 
Is ^ 00 

vo ~3- in 

CD CD O 

i— i 


invo h 
cd in is 

O -3- sf 
O O O 


ps co cd in 

Ps CO CO O 

vO CO 00 vO 
CD O CD O 


cu 

M 4J 

3 C l-i - 

4-1 CU CU 4J V 
CO 4J 4-1 CO O 
•H C K-l CU &, 
O O CO 4-> 

2 CJ 


o o o o 

co en h -h 

cm cd in co 

CM CM CM CM 


o o o 

Oi O CM 

CM CO O 
CM CM CM 


O O O 

\D \0 CM 

CD -3- -3- 

HN CM 


o o o 

CD — i ~h 

00 CM CD 

— 1 CM —t 


O O O O 
— i O 00 vO 

vO •* CO o 

CO CM CM CO 


O O O O 
vO CD -4 O 

00 00 <f CO 
CM CM CM CM 


O O O O 

OCAHH 

OONH 
CM CM CM CM 


O O O O 

in in o vo 
is o cd in 

-4CM -4H 


o o o 

vO -3- 00 

o cm in 

CO CO CM 


O O O 
O CD CM 

in in vo 

CM CM CM 


o o o o 
o m o cm 

CD co m ps 

CM CM CM CM 


w 

iJ 

H 


>s 

4-1 
>-, 1-1 K-l 
U CO O 

O C O. 
CU 

TJ 


vO CM m CM 
— i Is CD CO 

o co m co 

CD CD CD CD 


OiOh 

cd co oo 

ps co m 
cd cd cd 


cd co m 
r^ cd in 

co oo m 

CD CD CD 


<t in -^ 
CD 00 CO 

CD CD CD 


CD O 00 r-» 
CO —I CO CD 

CM CM vO O 
CO CD 00 00 


r-. vo cm vo 
m o m -^ 

CM 00 CM CM 
CD 00 CD CD 


enen is -4 
m cm -3- o 

CD O CO CO 
00 CD CD CD 


cd n oo rs 
vo m oo m 

00 CD vO o 
00 00 00 CD 


m CD o 
-3" vO O 

o m vo 

CD 00 CD 


00 CM O 

HOC* 

Is is -3- 
CD CD CD 


st cm -4 en 

■-4 CO -3- CO 

h in nn 

CD CD CD CD 




TJ HI 
CU l-i 
•H 3 t-l 
i-l CO CO 

ana 
a cu 
<: u 
a 


m o o o 
cm in in o 


m o o 
cm m o 


m o o 
cm in o 


m o o 
cm m o 


m o m o 
cm in r-~ o 


in o in o 
cm in r-* o 


in o m o 
cm in r^ o 


m o o o 
cm m in o 


moo 
cm in o 


in o o 
cm in o 


in o in o 
cm in rs o 




y 

•H >, 
K-l 4-1 
•H 1-4. 
CJ > 
CU CO 

a i-i 
en bo 


-o CO CO CO 

» co co co 

N CM N CM 


CO CO CO 
00 00 oo 

CM CM CM 


CO CO CO 

oo co oo 

CM CM CM 


CO CO CO 

co oo oo 

CM CM CM 


CO CO CO CO 

oo oo oo oo 

CM CM CM CM 


CO CO CO CO 

oo oo oo oo 

CM CM CM CM 


CO CO CO CO 
CO 00 00 00 

CM CM CM CM 


in in m in 
oo oo oo oo 

CM CM CM CM 


in in in 
oo oo oo 

CM CM CM 


in in in 
oo oo oo 

CM CM CM 


in in in in 
oo oo oo oo 

CM CM CM CM 


■i 


cu - 

H M 4J 

tO 3 C 

H 4J CU 4J < 
-> CO 4J O 

H 1-1 C CU 

s o o t 

-1 CJ 


-3 O O O 
» 00 -3- 00 

3- — i vD vO 
M CO CM CM 


o o o 

CD CO CM 

m co o 

CM CM CM 


o o o 
vo in cd 

cd m vo 

—I CM CM 


o o o 

CM -4 — i 

O CM CD 

(M CM -4 


o o o o 
—i oo oo cd 

*C -3 00 CM 
CO CM CM CO 


o o o o 

vO O -4 -3 

00 — i -3 1 r~ 
CM CO CM CM 


O O O O 
O CD -h 00 

vO O CM CM 
CM CM CM CM 


o o o o 
m in o is 

is o cd m 

— 1 CM -H -* 


o o o 

vO-3 CM 

O CM — i 
CO CO CO 


o o o 

00 O is 

in is o 

CM CM CO 


o o o o 

00 — 1 CD CM 

O st \0 is 
CO CM CM CM 




to o e 

•H TJ i-l l 
4J i-l 4-1 C 

i-l O CO 

C > P C 
I-l 


MOHCO 
n oo -3- oo 

MXIOON 




co is <f 
O CD <f 

oo is oo 


-3- vO CD 
-3- 00 >3 
oo r^ oo 


CM CD m 
CM \D ~h 
CD r^ oo 


-i co m h 

CO —I sf CO 
— 1 CD O O 


CD CD r^ 
O -h O -I 
CD O CD CD 


CO CO O CO 

Mnoio 

CD CD 00 00 


VO vD COst 

o ao <r vo 

O CD O CD 

t— 1 .—1 


Is vO CO 

vo is in 
CD O 00 


— i •* in 

CO CO is 
O0 00 00 


CM ps in 00 
in VD CM CM 
CD 00 CD 00 


c 

4 
1 


1 

H i-l - c 
.-1 C v 
■1 O O c 
J CO iH C 
H C 4J -H C 

: o co 

4 CJ Tj 


o -3- cm cd 

D r^ co ai 
3 O O O 

3 111 


CM 1 — CD 

inuis 
o o o 

1 1 1 


o oo in 
-3- m r^ 
o o o 

1 1 1 


-3- vO — i 

-J \0 co 

O O O 
1 1 l 


m p~ r~ — i 

vD \0 O CM 
O O -H — 1 

1 1 1 1 


o r-~ in cd 

vO CD O CD 
O O — i o 

1 1 1 1 


CM CD vO >3* 
NCOMIO 
O O O O 

1 1 1 1 


is m o oo 

<• m m co 
o o o o 

1 1 1 1 


<• CD CO 
vO 00 CD 
O O O 

1 1 1 


is —I CM 

CO is CD 

o o o 
1 1 1 


00 vO O — i 

in rs vo oo 
o o o O 

i i i i 




cu 

■-I 

en 


i cm co <r 


m \o n 


00 CD O 


—1 CM CO 


-^ m von 

-H _H ^H ~4 


00 CD O —I 
—i •—! CM CM 


CM CO <t m 

CM CM CM CM 


vO Is co CD 
CM CM CM CM 


O — l CM 

CO CO CO 


co -3- in 

CO CO CO 


vo rs oo cd 

CO CO CO CO 



19 



en 

00 



o 

o 



in 
on 



o 
m 



on 
o 



m 


-3- 


O 


en 




go 


O 


O 




ON 


on 


c- 


nO 


in 


O 


p^ 




O 




r~ 


X' 




O 


r-» 




p^ 


on 


m 


r— 


<r 


CM 


-a 


ON 


cn 


m 


en 





en 


en 


0O 




en 


en 


00 


P- 


vC 






00 


— 


p^ 


-a 


X 


en 


O 


O 


nO 


<r 


m 


— ' 


— ■ 


•-* 


O 


CO 


^o 


on 


<T 


o> 


*"* 


vO 


00 


en 


<r 


en 


On 


00 


m 


r-» 


in 


en 


O 


p^ 


— ' 


on 


en 


NO 


-a 





1-1 


r-* 


-- 


_ 


_ 


p^ 


O 


cn 


-a 


r^ 


0> 


ON 


UI 


p^ 


ao 


On 


oo 


91 


<T 


O 


en 


■a- 





CM 


<r 


ON 


en 


p^ 


r^ 


X 


<r 


^0 


CM 


r-. 


r*. 


<r 


r^ 


_ 


cjn 


^N 


•a- 


00 


ON 


in 


CM 


^o 


m 


0> 


On 


<y> 


on 


O 


= 


O 


= 


Z 


CM 


- 








Cf> 


CM 


O 






O 













O 


O 


ON 





ON 


O 





ON 





O 


1 ' 




CM 


CM 


1 ! 


CM 






1 ' 


CM 


O 


X 


c 


oo 


cm 


<J- 




O 


vO 


On 


nO 


N 


X 


-a 


p*- 


en 




p^ 


O 


CM 




O 


On 


O 




-3- 


en 


<r 


1O 


en 


P~ 


00 


^f 


ON 


CNl 


p^ 


O 


•a- 


r? 


r*. 


r"» 


CM 


00 


NO 


en 


-a 


r*. 


r~ 


— 


in 


co 


■» 


co 


— ■ 


CM 


en 


nO 


vO 


cn 


r~- 


-j 


X 


ON 


— ' 


— 


•» 


Ol 


en 


P» 


— * 


— ' 


r~ 


<f 


vO 


in 


00 


-a 


r^ 


CM 


ON 


00 


-a 


— ■ 


eM 


in 


00 


ON 


l-~ 


ON 


CO 


_ 


cn 


X 


On 


-a 


0* 


-a 


nO 


cn 


on 


O 


.~ 


cn 





-a 


cn 


X 


in 


_ 


en 


«a) 


>a 


CM 


CM 


_ 


<r 


ON 


CN 





CM 


en 


en 


CM 


CM 


On 


en 


_< 





St 


en 


en 


,_, 


m 


O 


tM 


cm 


-a 


in 


'" 


CM 


~* 


en 


m 


in 


nO 


CM 


m 


m 


p^ 


CM 


-a 


vO 


r-~ 


CM 


»a 


nO 


r^ 


CM 


-a 


vO 


r^ 


CM 


CM 


<r 


NO 


co 


CM 


<r 


NO 


m 


00 


CM 


<r 


m 


NO 


00 


CM 


■* 


NO 


00 


On 


X 


p-» 


p*. 


in 


en 


x 


r*. 


X 


CM 


p^ 


N 


cn 


oo 


CM 





O 


oo 


ON 


cn 


in 


. 


in 


on 


^ 


p^ 


CM 


NO 


00 


O 


<r 


CM 


on 


•ON 


ON 





00 


ON 


in 


ON 





ON 


en 


O 


O 


-. 


m 


— 


oc 


-a 


-a 


nO 


r-* 


r-* 


nO 


co 


H 


ON 


in 


in 


X 


CM 


en 


vO 


m 


cn 


O 


— ' 


ON 


ON 


CM 


00 


r^ 


m 


O 


<r 


-a 


NO 


>* 


00 





in 


en 


—• 


P^ 





en 





O 


O 


_ 


vO 


r* 


On 


_ 


-» 


en 


nO 


co 





00 


X 


r*- 


_ 


<r 


er» 


O 


-a 


on 


on 


CM 


vO 


m 


<r 


O 


VO 


ON 


CN 


co 


^D 


en 





>» 


<r 





-a- 


m 


r-. 


CM 


m 





ON 


vO 


O 


O 


in 


en 


cn 


CN 


-a 


00 


h« 


r^ 


p^ 


on 


r-* 


X 


ON 


00 


-a 


en 


in 


vO 


r-~ 


m 


m 


r~ 


CO 


r*. 


r-» 


m 


<f 


<r 


m 


d 


<r 


m 


CO 


>3- 


^n 


m 


00 


ON 


ON 








NO 


r** 


O 


O 



N 


~ 


^4 


P- 


m 


-~ 


X 


•a- 


— 1 


— . 


NO On 


ON 


in 


m 


CM 


<r 


in 


00 


en 


X 


ON 


NO 


~H 


ON 


NO 


CM 


X 


i/N 


r** 


en 


CM 


CO 


en 


-a 


en 


m 


ON 


m 


O 


CM 


p- 


m 


ON 


r-* 


in 





N 


— 


ao 


P»- 


•a- 


m 


a 


en 


-a en 


-r 


en 


en 


CTN 


CM 


NO 


— ' 


^c 


r-» 


■a- 


en 


<r 


ON 


CM 


00 


r*s 


ON 


m 


-a 


00 


ON 


en 


NO 


00 


On 


CM 


m 


ON 


NO 





r^ 


— 1 


cn 


en 


«t 


CM 


oo 


en 


X 


IS 


NO 


in 


-a 


on -a- 


en 


NO 


00 


CM 


in 


CM 


NO 





ON 


-a- 


NO 


vj- 


O 


NO 


m 


ON 


CM 


cn 


NO 


p^ 


CNJ 


O 


00 


CM 


On 


r*» 


NO 


CO 


NO 


CM 


p~ 


NO 


O 


On 


ON 


On 


at 


ON 


ON 


ON 





a 


O 


on 


■_■ 





oo 


ON 


On 





ON 


O 


X 


ON 


ON 





O 


ON 


ON 


X 


O^ 


ON 


ON 


ON 


ON 


ON 


ON 


O 


On 





O 


O 


- 


O 


ON 


O 


^ 



0000 000000 0000 0000 0000 0000 00000 00000 00000 0000 

r-* so ct* \0 < 00 00 00 -< O ciN -h iri in \c \D in n «j n^ in on in n o^-Nt n 00 ^HOr^<r^H 00 o vo ^ m o^(^cooo 

\ommo (s »- 00 o> n 00 <r o ir*> <r r^<rr^^^ m m o *o <r o om» m vo c^ tN <t \D in <r mO >x> inN^o-Na-r-^CT^ co^o-<tcM 

— — — — — ■ CM CM — ' M IN M tN N N ^h^h^hCM CnJ^hcMCnJ CMCN^H^h ^^^h^^h ^^^^^^^_<^^ CSjCsjr>J^^^H H (M IN fv) 

e^CTvr^in r-« ^ >o f^ n o OOOr^. o^ <*** cn \o o- n r% m on p*> «-i oo vO 00 vo m o> m »— 1 co cn co in o »o -^ vC 00 00 r*. c^ 

ri n - * <r o<r--cnos£) in in s 00 ^rinm-NNj \o 00 00 o> in in co 00 vu in in in -j vo ro h n nO ^ -h n 00 ■vf o n -vt n 

<n\CsCX c» f^ -j 00 ^ -nnT csir>.^in mvocoo ocsicnco n 00 m o oj<tr^\ocjs n n --< cm in inooooo n 00 ro o 

33 X X X X CJ 1 X O^CMT ^ 0> O 0> OOCOCOOv On ON 00 CO (T> & & <T* ON CO CO CO CO ONQOONCTsON OnOOOO ONCOOnO 



in o »n o 
cm m r*. o 



in in o in in o 

cm (M in n n o 



in o in in o 
cm m r-* r-*. o 



m 


in 


." 


m 


in in 


in 


in in 


m 


m 


in 


in in 


CM 


~J 


CM 


CM 


CM 


') 


CN 


CM 


CM CM 


CM 


CM 


CM 


CM 


CM 


r\l 


CM 


CM 


CN 


CM 


CM 


CM 


CM 


Cl 


CM 


CM 


CM 


en 


en 


m 


m 


X 


■ 


X 


00 


ec oc 


X 


oc 00 


ao 


00 


X 


00 ao 


00 


X 


oo 


00 


00 


X 


X 


00 


00 00 


00 


00 


00 


co 


00 


X 


00 


00 


X 


X 


X 


OO 


00 


X 


X 


CO 


00 


00 


CO 


CO 


CO 




-. 




CM 


CM CM 


CM 


CM CM 


CM 


CM 


CM 


CM CM 


C-J 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM CM 


CM 


CM 


CM 


CI 


rJ 


CM 


CM 


CM 


CM 


CN 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CNJ 



a 


a 

z 


O 
on 




NO 




m 


O 

X 


a 

CO 


O 

X 


c 






O O 

in m 


O 

' 1 


O 
in 


O 
in 


□ 

NO 


O 
NO 


O 
NO 


O 
nO 


c 



O O 

■j- -a 




-a 


O 
O- 


O 

cn 


O 


O 
On 



--r 



CN 




CM 


O 
on 






in 






-a 


O 


O O 

00 CM 


O 


O 
-7 


O 
m 




—1 ON 


O 

00 


O 
CM 


0> 


en 


en 





-a 


NO 


DC 


C i 


— 


00 

CM 


in m 

CM CM 


O 


-a 

CM 


p^ 


-T 


P^ 


CM 


nD 
CM 


On 


no 

CM CM 


p~ 

CM 


O 
CN 


n 


00 


m 


O 


o< 


en 


-a 


NO 


CM 


-a 


:D 


NO 


in no 

CM CM 


-a 

CM 


r^ 


CM 
CM 


O NO 

CM CM 


-a 

m 


O 

cn 



-a c c — 
x -o .0 — 

o c o o 



00 in *a on sO — 1 

O- O — O rn 00 
CT* s **i OC 00 00 



— « in o*n nnO 
cm n n in 
o> 00 00 00 



ON <J" On vO 

onx-w* 

— O ON ON 



•^ nO ON ON 
<J ON ONN 
ON CO O ON 



r-NN, \o r^ r^ 
O 00 <t co 
on r*-. 00 on 



o 00 ^ n vO 

ON o O O ON 



O ^-O CM ON — « 
ON O ON ON CO 



O on nO no n 
in in in <r cm 
00 n in. rs vO 



OHOfO 
CM o on in 
00 O 00 r^ 



00 00 -O On 

0000 



- •? O NNrt 

in in c* n n on 
c o o o o o 



ON 


<o 


r 





-a 


DO 


On 


ON 


r~ 


PN* 


-a 


00 


— 1 


m 


NO 


nO 


en 


X, 


90 


m cm 


NO 


c 


oc 


On 


m 


CI 


C 


— | 


m 


r** 


NO 


in 


-a 


m 


1/1 


m 


cn 


m 


in 


r-» r~ 


c 








O 


O 


a 


O 


— 1 


O 





O 











O 


O 











O O 



en —1 -a in o 
m no in no p*» 
OOOOO 



00 r» on -a o 
^a no in p~ r~ 
00000 



00 -a 00 m 

<f On — < 00 
O O -< O 



-a* in x p^ 00 on 
~a -a -a -a ~a -a 



00 On O — 

in in no no 



cm m -a m 

NO vO ^o NO 



NO p~ 00 ON o 
p^. p^. p-. r-- 00 



20 



a 

o 
u 

i 
i 

a 



o 

JO 

cd 





c 
o 
























co 


































CO 








•H 


•H 






~H 






o 






CO 


















On 
















1-^ 




NO 




CO 


CO 






•* 






l-~ 






00 








O 










r~ 








o 






m 




CM 




a) 


Q. 


































































j= 








in 






NO 
















o 










o 








o 










in 




o 












































-H 






















r-l 


c 


































































cd 


o 


« 
































































a 


•H 


01 


bo 




00 






oo 






NO 








i-H 










ON 








o 






00 




CM 


u 


4J 


i-l 


0) 




ON 






r~ 






o 








ON 










<r 








m 






NO 




CM 


0> 





B0T3 






• 








• 








• 








« 










• 










• 






• 




• 


4-1 


1-1 


c 






in 






<r 






00 








i-H 










CM 








ON 






CO 




m 


c 


p 


CO 






CO 






CO 






CO 








-tf 










CO 








CO 






CO 




CO 


M 


y-j 




































































co 


14-1 


































































3 


o 


































































•H 




S-n 




o 






*-H 






NO 








•-H 










in 








o 






NO 




CM 




C 


1-1 


4-1 




CSI 






CM 






CM 








CM 










o 








m 






r~ 




00 




v 


O 


01 




nO 






00 






i-i 








■* 










—* 








m 






ON 




m 




rH 


4-1 


D-i 
































































.-1 


CJ 


cd 


































CM 
























0) 


cfl 


CO 
































































tl- 


in 






























































/— — ^__ — , 






>> 




NO 


r-~ 


00 


CN 


^_, 


in 


ON 


CM 


NO 


r-~ 


CO 


r-~ 


CM 


CO 


r^ 


NO 


ON 


CM 


CO 


<r 


CO 


r~ 


oo -a 


ON 


-a- 


00 


-a- 


CO CO NO CO 


NO 


cm cm in on on 






4-1 




o 


CNJ 


oo 


00 


I — 1 


t» 


NO 


NO 


r— 1 


O 


CO 


o 


NO 


CM 


NO 


i — 1 


oo 


-* 


00 


O 


CO 


O 


o sr 


■ — \ 


oo -<r 


i — i 


r^ — i o m 


o 


no cm in r^ ~h 




4-> 


•H 


in 
































































cu 


CO 


o 


nO 


co 


CN 


CM 


r^ 


i — i 


co 


NO 


CO 


r>» 


00 


co 


ON 


00 


■ — i 


<r 


CO 


CO 


1 — 1 


ON 


r— 1 


00 


co -a- 


co 


r~ 


m 


NO 


cm on m o 


m 


on no -a- —4 CM 




3 


tu 

T3 


a. 




CN 


CM 


CM 




CM 




o 








CM 






CM 






CM 


CM 




CM 














-* O -" — I 




rt HrtCNl H 






CO 




00 


n 


nO 


in 


<3 


m 


00 


CM 


CM 


CM 


co 


1— 1 


00 


o 


O 


ON 


r~ 


O 


o 


ON 


NO 


o 


NO o 


00 


nO 


CTN 


CO 


N -4 CI H 


m 


-3- CO 00 nO -3- 




^ 


CO 


i-i 


o 


o 


00 


CO 


-3/ 


CO 


oo 


NO 


NO 


NO 


CO 


r^ 


00 


m 


i-H 


nO 


<r 


NO 


-H 


00 


CO 


m 


CO -H 


CM 


r^ 


CO 


CM 


cm oo on m 


CM 


-3- oo —i co in 




CO 


0) 


to 
































































0> 


I-l 


a 


nO 


o 


O 


CO 


CM 


in 


00 


r~ 


ON 


ON 


CO 


ON 


O 


NO 


ON 


NO 


NO 


NO 


ON 


NO 


00 


-a- 


O ON 


NO 


in 


<r 


O 


oo —i -a- on 


oo 


cm -3- -h oo m 




P-. 


4-1 
CO 




CN 


in 


r~. 


00 


CM 


<r 


m 


r~- 


CO 


CO 


in 


r-~ 


CM 


CO 


CO 


NO 


00 


CM 


CO 


<r 


in 


i-^ 


CM CO 


in 


in 


CO 


00 


-h CO co -a- 


NO 


cm <• -3- m r^ 


r-l 

cfl 


CO 


. 




. 


o 


NO 


NO 


ON 


o 


r-~ 


00 


00 


CTN 


CO 


ri 


o 


o 


<r 


NO 


^ 


o 


l _ mt 


o 


o 


m 


CO 00 


CM 


^ 


o 


00 


o o o o 


o 


~3- no <f O ON 


•H 


1- 


c 


4-1 


00 


r^ 


m 


-4t 


oo 


O 


CO 


CM 


O 


CN 


«* 


CO 


CM 


o 


m 


ON 


r~ 


o 


CO 


o 


o 


ON 


o -a- 


r^ 


r^ 


ON 


CM 


o o o o 


o 


no cm -3- ~a -a- 


4-1 


3 


o 


o 






























































•H 


4-1 


•H 


a 


in 


<r 


CN 


t— 1 


o 


o 


00 


CO 


NO 


. — 1 


NO 


oo 


NO 


o 


r-» 


o 


O 


o 


CM 


o 


o 


NO 


OO — 4 


m 


n 


co 


CO 


o o o o 


o 


r-^ o in no -3- 


c 


CO 


4-1 




nO 


00 


ON 


<f 


00 


o 


00 


NO 


r-- 


ON 


oo 


ON 


00 O 


co 


r^ 


r- 


O ON 


o 


o 


ON 


ON 00 


CO 


oo 


ON 


ON 


o o o o 


o 


on i — r^ on no 


M 


to 
















^H 
















1-1 








"■• 




— 1 


"* 














~* — 1 r— » . 1 


* H 




1 






>> 


m 


co 


o 


CM 


CO 


NO 


m 


CO 


m 


in 


m 


, 


r-~ 


in 


m 


o 


•j- 


-* 


CO 


NO 




m 


^ r~- 


CO 


ON 


<r 


O 


m co r^ on 


CM 


r- -* -3- m -a- 


t-l 


•a 




4-1 


on 


i — i 


NO 


CO 


co 


ON 


CN 


CM 


ON 


CM 


o 


o 


<■ 


oo 


CTN 


00 


CO 


O 


1 — 1 


r^ 


r— 


-3- 


r~ O 


■ — i 


NO 


NO 


ON 


O CM CM 00 


<T 


r^ 00 CM -3- o 


O 


a) 


>,tI ' 






























































CO 


J-> 


U 


CO CJ 




nO 


CO 


O 


00 


<* 


in 


CO 


in 


r^ 


<r 


o 


o 


o 


<r 


ON 




-a- 


«* 


<r 


00 


•a- 


<r oo 


CO 


i-H 


CO 




on cm m -a- 


CM 


CO CO ON 00 •— ' 


c 


CO 


T3 


C Cu 


o 


O 


o 


•— I 


ON 


o 


o 


ON 


On 


ON 


o 


~H 


o 


o 


o 


On 


O 


o 


o 


o 


o 


o 


On ON 


o 


o 


o 


O 


00 On ON ON 


O 


O O On O O 





-o 




01 






























































o 






TJ 






























































a' 




































































u 


4-> 


































































3 


a 


U 


* 


o 


o 


o 


o 


o 


o 


o 


o 


O 


o 


o 


o 


o o 


o 


o 


o 


o 


o 


o 


o 


o 


o o 


o 


o 


O 


o 


o o o o 


O 


O O O O O 


4-1 


01 


0) 


4-1 4J 


CO 


r< 


CN 


r- 


oo 


<r 


CM 


1 — 1 


o 


o 


<r 


CM 


~i- 


<r 


CM 


CO 


CM 


00 


CM 


<f 


r^ 


NO 


cm ~a 


ON 


CM 


m 


CM 


CM -3- CO O 


o 


on no in oo co 


CO 


4-) 


4J 


CO CJ 






























































•.-4 


c 


y-i 


oi a 


oo 


CN 


<r 


CO 


co 


CO 


<r 


oo 


NO 


CM 


CO 


CO 


NO 


00 


CO 


o 


O 


CM 


<r 




<r 


m 


o -a- 


CO 


<r 


<r 


00 


oo oo no oo 


CM 


CM O — i ~-> O 


o 


o 


cd 


4-1 


—- ( 


CM 


CM 


CM 


CM 


CM 


CM 


1 — 1 


CM 


CO 


CM 


CM 


CM 


CM 


CM 


CN 


CM 


CM 


CM 


CM 


CN 


CM 


CO CM 


CM 


CM 


CM 


CM 


CO CO CO CO 


CO 


CM CN CM CM CM 


53 


CJ 






































































>-. 




On 


r^ 


CO 


O 


ON 


NO 


p~- 


oo 


,_, 


ON 


•* 


ON 


-a- 


00 


NO 


^ 


m 


O 


ON 


^D 


ON 


_, 


in On 


ON 


CO 


nO 


ON 


n in h on 


NO 


co r-. oo on no 






4-1 




nO 


<r 


ON 


o 


m 


NO 


m 


CM 


oo 


NO 


ON 


00 


NO 


O 


r^ 


U"l 


r~ 


m 


o 


O 


CM 


O 


00 ON 


CO 


00 


r^ 


m 


m oo -a- o 


I— 1 


CM CO CM ON CM 




>.-rt 


M-l 
































































U 


CO 


o 


r^ 


o 


CO 


m 


-3- 


OO 


m 


o 


ON 


00 


in 


ON 


<r 


CN 


co 


<r 


-3- 


o 


oo 


CO 


r-~ 


>* 


NO ~H 


in 


■* 


CM 


o 


-icOntO 


r~ 


r*~ no -3" on co 




o 


4) 


a. 


en 


o 


ON 


ON 


ON 


ON 


ON 


On 


00 


CO 


ON 


On 


ON 


ON 


ON 


ON 


ON 


o 


ON 


ON 


On 


On 


00 ON 


on 


ON 


On 


ON 


oo i — oo oo 


00 


ON ON ON ON CJN 




XI 


CD 


































































CI) 


S-i 


































































•H 


3 


•H 


in 


o 


m 


o 


m 


o 


n 


o 


m 


o 


in 


O 


m 


o 


o 


m 


o 


in 


o 


o 


in 


O 


in o 


m 


in 


o 


o 


m o o m 


O 


m o o m o 




.-1 


CO 


CO 


CM 


U0 


r^ 


o 


CM 


in 


r-» 


o 


CM 


in 


r- 


o 


CM 


in 


m 


r^ 


o 


CM 


in 


in 


r— 


O 


cm in 


r~~ 


p«. 


o 


o 


cm in m r~ 


o 


cni mms o 




a 


CO 


Cu 








rt 








~H 








1— 1 










t— 1 










-H 








i-H 


.— 1 




.—1 


~H 




9- 


01 


































































<s 


U 


































































o 




































































•H 


>n 


































































NW 


4-1 




co 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


co 


CO 


CO 


CO 


co 


CO 


CO 


CO 


CM 


CM 


CM 


CM 


CM 


CM CM 


CN 


CM 


CM 


CM 


CM CM CM CM 


CM 


CM CM CM CM CM 




■H 
O 

o> 


•H 
> 

cd 




oo 


00 


oo 


00 


00 


00 


00 


oo 


oo 


00 


oo 


oo 


oo 


00 


00 


00 


oo 


00 


00 


CO 


00 


00 


00 00 


00 


CO 


CO 


00 


00 00 00 00 


oo 


oo oo oo oo oo 






CN 


CM 


CN 


CN 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM CM 


CM 


CM 


CM 


CM 


CM CM CM CM 


CM 


CM CM CM CM CM 




o, 


i-i 


































































w 


bO 


































































a) 


^ 
































































H 


u 


4-1 
































































cd 


■s 


a 




o 


o 


o 


O 


o 


o 


O 


o 


O 


o 


O 


O 


o 


o 


o 


O 


o 


o 


o 


O 


o 


O 


o o 


O 


O 


O 


o 


o o o o 


O 


o o o o o 


i-i 


4-1 


01 


4-1 


00 


r* 


1-^ 


CO 


00 


CO 


m 


-* 


o 


o 


r^ 


r^ 


-tf 


NO 


<f 


00 


NO 


o 


<r 


-* 


in 


O 


r^ -a- 


r^ 


O ON 


CM 


in r~ in oo 


in 


O nO CM O CO 


4J 


CO 


4J 


O 






























































•H 


•H 


c 


a. 


00 


CN 


m 


ON 


-d- 


o 


NO 




NO 


CM 


m 


NO 


NO 


CO 


-cr 






o 


i-^ 


CO 


O 


o 


in no 


in 


NO 


ON 




CO NO H CM 




00 O CO nO o 


C 


o 


o 






CM 


CM 


CM 


CM 


CO 


CM 


CM 


CM 


CO 


CM 


CM 


CM 


CO 


CM 


CN 


CM 


CO 


CM 


co 


CO 


CO 


CO CM 


CM 


CM 


CM 


CO 


-a- -a- <a- -a- 


<f 


CM CM CM CM CM 


H 


1 


CJ 


































































i-H 




































































CO 




o 


00 


00 


NO 


o 


CO 


—H 


CTN 


r-~ 


r-^ 


CM 


CM 


ON 


|-~ 


ON 


CTN 


CTN 


m 


CN 


r- 


m 


ON 


CO 


r~ -a- 


m 


m 


CO 


CO 


oo co no oo 


o 


OVM-. H CO 




i-l 


XI 


•H 


o 


m 


00 


o 


NO 


ON 


<r 


in 


NO 


CTN 


<r 


NO 


NO 


1— 1 


CO 


NO 


NO 


in 


co 


on 


o 


r~- 


CM —I 


<r 


m 


ON 


•a- 


in co oo on 


CM 


O CM NO nO 00 




4-> 


■H 


4-1 


oo 


f~ 


r» 


o 


00 


r~~ 


CO 


ON 


ON 


ON 


oo 


r~ 


00 


ON 


r^- 


00 


oo 


r~. 


00 


f~ 


oo 


00 


O ON 


CO 


CO 


00 


ON 


-h CM O —l 


O 


CO CO CO N CO 




■H 


o 


cd 


































































> 


u 


o 






CM 






































^ H 
















^H 


1 

•H 








CO 


in 


O 


oo 


o 


CM 


^ 


-d- 


00 


CO 


CM 


00 


t~» 


ON 


CO 


m 


-d- 


CO 


<r 


m 


O 


CO CM 


in 


r~ 


in 


^ 


-3- in -3- nO 


ON 


CM CM O OO r-» 


to 


r-( 


c 




<r 


in 


<r 


O 


CNO 


nD 


On 


oo 


NO 


CO 


r^ 


on 


m 


oo 


m 


m 


NO 


CO 


m 


nD 


o 


O 


00 nO 


r- 


nO 


o 


-H 


oo -3- —i m 


-a- 


no r^ in r*» r^ 


•H 


O 







o 


o 


o 




o 


o 


o 


o 


o 


o 


O 


o 


o 


o 


o 


o 


o 


O 


o 


o 


—4 


.— i 


O O 


o 


o 


i— 4 


f— 1 


o — i —i — i 


*—* 


o o o o o 


-4-1 


CO 


•H 


c 






























































1-1 


B 


4-1 


•H 


o 


i 


i 


1 


1 


1 


1 


1 


1 


1 


1 


1 


i 


i 


I 


i 


i 


i 


i 


1 


1 


i 


1 1 


i 


1 


1 


1 


i i i i 


i 


1 1 1 1 1 


c 


o 


cd 




i 




























































M 


CJ 


"O 




































































0) 




































































o. 




m 


NO 


T-* 


00 


ON 


o 




CM 


CO 


-* 


m 


NO 


r~ 


00 


ON 


o 




CM 


co 


-* 


m 


NO 


r^ oo 


ON 


o 




CM 


co -a- m no 


r^ 


00 ON O -< CM 







CO 
W 




00 


00 


00 


00 


00 


ON 


CTN 


ON 


ON 


ON 


ON 


ON 


ON 


ON 


ON 


o 


o 


O 


o 


o 


o 


o 


o o 


o 












rt HNCM CN 1 



21 



CO 
CO 
CO 



S3 

00 



S3 
o 



CO CO «/"* i/^ 00 



st 


OB 


- 


© 


uo 


-3 


on 


o 


CM 


lO 


CM 


p** 


in 


<r 


X 


CO 


On 


CM 


vO 


iC 


<r 


<r 


co 


<r 


ST 


go 


CO 


o 


CO 


•* 


s3 


o 


CM 


O 


CO 


MO 


CO 


m 


m 


m 


CO 


M0 


CM 


O 


CM 


•* 


ps 


ST 


uo 


ps 


ac 


— 


•* 


M3 


in 


CM 


in 


ps 


o 


** 


— 


ps 


on 


CM 


o 


X 


in 


oo 


r- 


<r 


en 


oo 


S3 


«* 


<r 


ON 


<r 


MO 


st 


CM 


on 


MO 


m 


CM 


CM 


~3 


ON 


MO 


cc 


MD 


Ci 


CO 


_ 


^j. 


o 


o> 


_ 


Cf> 


p^ 


in 


cm 


CO 


O 


in 


_ 


m 


_ 


_ 


co 


c 


ps. 


in 


o 


CM 


O 


C| 


CM 


_, 


Ps 


O 


CM 


_, 


0\ 


on 


o 


CM 


nO 


O 


OO 


CO 


m 


Ol 


CTN 


^.o 


p*» 


BN 


S3 


mo 


p ^ 


cc 


■ 


st 


UO 


'"*■ 


CM 


sT 


MO 


CO 


CM 


s3 


c 


00 


CM 


^-r 


CO 


m 


ps 


CM 


<r 


MO 


r-« 


00 


CM 


<r 


N© 


p~ 


CM 


CO 


m 


00 


CM 


CM 


uo 


M0 


MO 


00 


CM 


CO 


m 


r^ 


LO 


X 


^ 


in 


CM 


in 


er> 


X 


<r 


in 


CM 


S3 


CO 


r*~ 


in 


p-s 


oo 


sT 


ps 




X 


m 


M0 


sr 


CO 


X 


p~- 


00 


O 


o 


in 


O 


CM 


MD 


<r 


00 


CM 


O 


mo 


CM 


-3 


r- 


CO 


ON 


«* 


S3 


1— 


r 


^ 


— 


MO 


ST 


— ■ 


CO 


CO 


uo 


cm 


co 


oo 


X 


mc 


M0 


ps 


in 


— 


vO 


CO 


-3 


<T 


<r 


*» 


on 


CM 


ps 


r- 


CM 


in 


vO 


rs 


CM 


oo 


— ' 


ps 


M0 


<r 


CM 


rt 


<r 


— 1 


O 


_< 


_ 


X 


o> 


CO 


_, 


N 


sT 


in 


-3- 


- 


.- 


on 


O 


o 


•» 


M0 


oo 


CO 


<r 


_* 


m 


CO 


ifi 


ro 


X 


CO 


ps 


_^ 


O 


m 


o 


O 


ON 


-3 


00 


m 


_< 


en 


^ 


CM 


M0 


O 


o 


CO 


X 


X 


ps 


rs. 


On 


S3 


JO 


JO 


-a- 


<r 


MO 


CO 


S3 


in 


MO 


X 


ps 


-3 


CM 


U"> 


U"l 


<r 


CO 


CO 


I/O 


MS 


ps 


co 


CO 


10 


r~ 


MO 


X 


CO 


ps 


co 


CO 


M0 


ps 


•X 


o> 


CO 


CO 


00 


oo 


mo 


X 


■Z 


CO 


o> 


ao 


a 


U0 




co 


uo 


MS 


S3 


in 


in 


<r 


S3 


CO 


O 


CM 




00 


o 


JO 


CO 


o 


00 


CM 


m 


CO 


o 


CO 


CM 


CO 


co 


ps 




m 


m 




M0 


CO 




^o 


oo 


-C 


~~ 


z 


S3 


in 


— ' 


X 


,H 


"~* 


~~* 


CO 


st 


CO 


m 


~* 


MO 


CM 


co 


m 


~~* 


o> 


m 


ps 


CO 


ifi 


oo 


in 


P~ 


co 


v£> 


M3 


CO 


r^ 


r^ 


m 


m 


CO 


o> 


CO 


CO 


-3 


On 


CO 


UO 


o> 



c~ r^ r^«. *n 


u-\ <r m o> 


in o> <r 


en 


O -3- co en oo 


CO CT» O 0> 


o*\ o cr* o> 


CMJnO 


o 


C7\ O^ C^ O^ CT^ 



c 


a 


C 


- 


o 


O 


O 


a 


o 


O 


C 


a 


O 


O 


O 


CO 


o 


O 


o 


c 


O 


O 


o 


O 


o 


o 


o 


o 


O 


o o 


O 


o 


o 


o 


O 


o 


O 


O 


o 


o 


o o 


O 


o 


M0 


-~ 


t— 


o> 


ac 


in 


-3 


- * 


CO 


ON 


-~ 


CO 


co 


m 


CO 


-3 


— 


r~ 


C-! 


ON 


CM 


-^ 


■a 


r-~ 


lO 


— 


CM 


r^ 


00 


m oo 


CM 


CM 


CO 


■3- 


CO 


in 


CM 


MC 


CO 


o 


-H P~ 


— ' 


UO 


-3- 


<r 


in 


-. 


CO 


00 


o 


CM 


CM 


~3 


X 


CO 


r-^ 


MO 


ON 


-3 


CM 


p^. 


X 


r^ 


_ 


NO 


CM 


CO 


r^ 


o 


ON 


m 


o 


—I CM 


_ 


<* 


m 


CO 


CO 


_< 


OO 


CO 


CO 


ON 


o m 


r- 


CJ 


-. 


-. 


c. 


CM 






CM 


-. 




~ 












CM 


CM 








" 


" 


~ 


^ 


^ 


CM 


" 


" 


^^ 


CM CM 


CM 


CM 


' 


CM 


" 


CM 




CM 


CM 


^ H 


•H CM 




CM 


PS 


I 


r*» 


pH 


j^ 


ao 


co 


~^ 


00 


P"» 


X 


CM 


1 


i 


o 


_^ 


CM 


o 


ts 


in 


ao 


CO 


<3 


o 


^^ 


^ H 


m 


^3 


_ H 


On <3 


MO 


r». 


_, 


in 


CO 


CO 


MD 


oo 


O 


MO 


mo in 


M3 


CM 


O 


~. 


-r 


e 


ao 


CM 


X 


<r 


On 


in 


vO 


-3 


— 


*"* 




co 


CO 


o 


c 


C-l 


in 


^ - 


" - 


vO 


MD 


m 


oo 


r^ 


"^ 


CO MO 


00 


m 


r- 


in 


ON 


CM 


r^ 


CM 


oo 


ON 


O ON 


vO 


O 



m o m o o 
cm in p- o o 



in o in o 
cm in p-^ o 



-. 


-. 


-■ 




CM 


CO 


co 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO CO 


-3 


-3- 


~3 -3 


-3 ~3 


-T 


<r 


-3- -3 


•Of 


<T 


«9 


<r 


-3- 


«ar 


<t 


-3 


X 


X 


er- 


as 


CO 


00 


X 


X 


oo 


00 


X 


X 


oo 


00 


DC 


X 


oo 


oo 


X 


X 


X 


00 


ao 


X 


X 


oo oo 


00 


X 


00 00 


oo oo 


00 


oo 


00 00 


X 


00 


00 


oo 


oo 


CO 


00 


00 










CM 


CM 


-1 


-; 


CM 


CM 


CM 


CM 


CM 


CM 


CJ 


CM 


CM 


CM 


n 


CM 


CM 


CM 


CM 


CM 


CM 


CM CM 


CM 


CM 


CM CM 


CM CM 


CM 


CM 


CM CM 


CM 


CI 


CM 


CM 


CM 


CM 


CM 


CM 



= 


CO 


CO 


o 


o 


o 


o 


— 


o 


O 


O 


CC 


o 


o 


a 


O 


o 


o 


o 


a 


O 


o 


o 


a 


o 


O 


o 


O 


o 


o 


o 


o 


o 


O 


o 


o 


o 


o 


o 


O 


a 


o o 


o 


O 


c 


UO 


CO 


o- 


CM 


in 


- 


- * 


ON 


ON 


—" 


CO 


en 


in 


CO 


-3" 


MO 


o 


c: 


ON 


a 


** 


o 


r^ 


M0 


— 


CM 


p^ 


00 


UO 


U0 


CM 


<r 


CO 


-» 


CO 


UO 


CO 


^o 


CO 


o 


CM P~ 


l£J 


OO 


- 


- 


-- 


^3 


UO 


00 


c 


ex 


MO 


-3 


X 


CO 


p^ 


M3 


ON 


-3 


CM 


ON 


00 


PS 





MO 


CO 


CO 


Ps 


c 


ON 


in 


o 


__ 


NO 


_, 


uo 


UO 


CO 


CO 


^, 


rp 


CO 


CO 


ot 


CO U0 


r^ 


UO 




-■ 


-. 




CM 




CM 


•. 


~" * 




~ 


~* 


_J 




"^ 


f 1 


CM 


~* 








^^ 


""* 


~* 


^^ 


CM 


~* 


' 


"" ' 


CM 


CM 


CM 


CM 


~* 


CM 


' 


eM 


"* 


CM 


CM 


CM 


— < CM 


CM 


CM 




~ 


- 


o 


CO 


r^ 


- 


o 


UO 


_ 


NO 


X 


CO 


00 


X 


r 


-3 


CO 


■r 


-3 


o 


UO 


o 


-3- 


r^ 


^ H 


UO 


MO 


00 


o 


o 


UO 


m 


CO 


UO 


__, 


p*» 


I 


^ H 


co 


ON 


MO rs 


po 


sD 


.' 


T 


■z. 


X 


■D 


UO 


-. 


-- 


uo 


UO 


f 


i 


oo 


— 1 


ON 


-* 


CO 


o 


X 


V\ 


-r 


O 


o 


O 


e 


CO 


CO 


ON 


o 


O 


o 


ON 


OO 


cr 


ON 


p- 


— < 


— < 


--r 


— i 


CO 


CO O 


I 


x. 


X 


00 


ON 


X 


r^ 


CM 


ON 


ON 


O 


ON 


DC 


O 


on 


ON 


at 


X 


ao 


- 


cr 


cr 


G 


o 


- 


a 


X. 


X 


ps 


- 


ON 


O 


o 


ON 


OO 


O 


00 


ON 


rs 


er 


x. 


oo 


Po 


O On 


CT 


CO 



r, ~ O C " ■ 

~* -' ac ao p** 



~ — CP -O 
UO JO p^ o- 

O T- CO CO 



00 CO JO CO 
^3 X 00 O 
O O O — 



O — • O lo 
CO MO Ps MO 

o o o o 



o ao o oo mo 

N ITI N Ps — 

o o © o o 



CM ON po O CM 
MO 00 00 00 M0 

o o o o o 



ps UO MO O 
S3 UO MO — * 

O O O -« 



sr -h is m 
uo ps p^ o 
o o o —• 



On 00 CO o o o 
st CO U0 U0 00 MO 

o o o o c o 



CO 00 — < CO 

in ps oo —i 
O O O — i 



EDO O — 


* . — -f lT 


^ r*. X iT 


O -^ eg <n -sT 


lA n-O f>K CO 0*v 


o ~^ r^i <n 


■»* tn ^ r^ 


-~ — 


*— "" [*! pH 


""■""■"*■'*■ 


*.T *sT -sT -T ^ 


-sT >sT <T <T <t 


m in in in 


in in in m 



22 





o 






































































ON 


















•H 


■H 








o 








t— i 






CM 






in 






CM 






00 






IN 








n. 










00 








CO 


CO 








-a- 








so 






-* 






O 






m 






^r 






oo 








00 










IN 








01 


a 










• 










• 








• 








• 








• 








• 








• 










• 










• 








o 
o 










CNl 
















OS 














in 






-a- 


























m 






•-< 


c 
























































































« 


o 


m 






















































































d 


•H 


<u 








-a- 








.—i 






sO 






00 






sO 






i — i 






^H 








r— 1 










IN 






u 


u 


.-1 


M 






CM 








OS 






sO 






r» 






CO 






CO 






o 








o 










-3- 






o> 





M 


01 








• 










• 








• 








• 








• 








• 








• 










• 










• 






4J 


1-1 


C 


T3 






in 








r^ 






vr 






sO 






00 






|N 






sO 








sO 










IN 






c 


u 


CO 








CO 








CO 






CO 






CO 






CO 






co 






CO 








CO 










CO 






H 


M-l 


























































































(0 


iw 
























































































3 


O 
























































































i-l 




>s 






CO 








oo 






00 






IN 






00 






oo 














sO 










in 








c 


M 


4-1 






in 








00 






CO 






I — 1 






t— 1 






CO 






CO 








.—i 










rN 








Q) 


o 


01 






CM 








CM 






o 






OS 






00 






in 






CM 








o 










r~ 








.-i 


4-> 


CH 






















































































^H 


CJ 


CO 
















. — I 






CM 














.—1 














i— I 








CN 










• — i 








<U 


CO 


CO 






















































































fe 


M-l 


























































































N, 




rN 


so 


_, 


CO 


O 


CO 


m 


_, 


OS 


sO 


o 


m 


m 


CM 


OS 


sO 


CNl 


CN 


<r 


o 


CM 


CM 


00 


ON 


Os 


CN 


CO 


OS 


ON 


ON 


00 


OS 


o 


CM 


sO 


CM 


CM 


o 


ro 


IN 


CM 






4-1 




Os 


rN 


00 


1 — 1 


m 


CO 


os 


CO 


. — i 


<r 


1 — 


m 


i — i 


-a- 


SO 


CO 


OS 


SO 


|N 


CM 


00 


ON 


co 


IN 


SO 


IN 


—4 


f— 1 


t-H 


CM 


IN 


<r 


o 


-a- 


CO 


•a- 


CO 


x» 


CO 


-3 


O 




4-1 


•H 


M-l 






















































































0) 


CO 


CJ 


! 1 


sD 


00 


CO 


CO 


in 


vO 


CO 


CM 


sO 


r-^ 


CO 


00 


oo 


IN 


m 


IN 


OS 


i — 1 


■ — 1 


1 — 1 


<— 1 


rN 


m 


IN 


sO 


m 


00 


sO 


sO 


oo 


sO 


OS 


IN 


<r 


oo 


00 


sO 


CM 


O 


•— i 




3 


C 
0) 

-a 


a 


o 






o 




O 








o 


O 


o 














o 


o 


o 
















o 




o 












o 




<N 


CM 


CM 






en 




<T 


n. 


00 


CM 


CM 


r-~ 


CM 


-* 


S0 


in 


o 


in 


00 


_ 


CM 


o 


00 


CM 


oo 


00 


CO 


^ 


■oo 


CM 


CO 


CO 


Os 


sO 


<r 


O 


sD 


_ 


CM 


CO 


OS 


ON 


sO 


CO 


■* 


CO 


ON 




^ 


co 


i-4 


<r 


on 


in 


OS 


m 


sO 


OS 


^H 


CO 


!■— 


sO 


CO 


00 


r— 


CO 


m 


CM 


O 


o 


rN 


.— < 


OS 


-a- 


CM 


m 


CM 


IN 


sO 


CM 


m 


in 


OS 


IN 


CM 


o 


IN 


OS 


-3 


CN 


m 


IN 




CO 


41 


CO 






















































































0) 


1j 


a. 


CM 


UN 


00 


OS 


r^ 


CO 




o 


CO 


O 


so 


m 


co 


os 


OS 


sO 


sO 


in 


sO 


CO 


in 


-a- 


CO 


CN| 


CN 


O 


00 


O 


in 


<r 


in 


sO 


•a- 


sO 


-a- 




CN 


rN 


m 


CN 






Pm 


4J 

co 




^1 


ro 


co 


m 


00 


1^ 


CM 


■* 


in 


oo 


CM 


«* 


m 


r-. 


^ H 


CO 


lO 


r-. 


CM 


<r 


sO 


00 


CM 


~a- 


sO 


00 


, " H 


<r 


in 


rN 


CM 


<r 


in 


m 


sO 


oo 


CM 


-a- 


m 


-o 


oo 


i-H 
CO 


CO 


. 




ON 


VO 


O 


OS 


<t 


r-~ 


sO 


r _ l 


00 


CM 


-* 


,_, 


o 


00 


CM 


o 


o 


O 


in 


Os 


CM 


-a- 


-a- 


IN 


CM 


-a- 


o 


o 


CO 


00 


so 


00 


O 


1 _ 4 


•a- 


o 


co 


CM 


<r 


m 


o 


•H 


Ij 


c 


4J 


OS 


O 


CO 


oo 


00 


O 


so 


oo 


CO 


o 


OS 


CO 


r^ 


r~ 


IN 


OS 


o 


O 


OS 


<r 


OS 


sO 


CO 


SO 


<r 


<r 


o 


o 


^H 


IN 


CM 


■ — t 


. — i 


CO 


CM 


o 


-a- 


00 


t— i 


fN 


o 


4-1 


3 


o 


CJ 




















































































■H 


4J 


■H 


a 


CO 


VO 


i — i 


CM 


CNl 


r^ 


i — i 


ON 


in 


sO 


OS 


in 


ON 


CM 


IN 


in 


o 


o 


CO 


<r 


<r 


-a- 


-a- 


O 


CO 


m 


-a- 


o 


OS 


ON 


oo 


sO 


in 


CO 


-a- 


o 


o 


o 


o 


-a- 


o 


C 


CO 


4-1 




<f 


in 


on 


m 


OS 


sO 


00 


r^ 


sO 


m 


m 


m 


OS 


oo 


OS 


OS 


o 


o 


m 


P0 


CO 


sO 


IN 


CO 


00 


OS 


ON 


o 


UN 


IN 


in 


IN 


OS 


OS 


IN 


o 


sO 


00 


ON 


CO 


o 


M 


ro 






































^ 


^ H 




















""* 
















~"* 










1-1 


1 






>s 


oo 


OS 


rN 


in 


r-^ 


CM 


so 


cni 


o 


CO 


00 


-a- 


CM 


CO 


00 


o 


^ 


^ 


sO 


m 


IN 


r» 


m 


00 


IN 


m 


00 


o 


CO 


CM 


00 


ON 


-a- 


00 


<r 


^ 


IN 


<r 


■a- 


o 


00 


.-1 


T3 




4-1 


m 


CM 


CO 


O 


vO 


CO 


O 


Os 


r^ 


00 


~H 


OO 


sO 


-a- 


m 


sD 


sO 


oo 


OS 


CM 


co 


-a- 


-a- 


. — 1 


CM 


m 


|N 


o 


in 


-3- 


t-H 


CO 


. — i 


-a- 


rN 


oo 


IN 


sO 


OS 


-a- 


CM 


O 


0) 


><n n 




















































































CO 


4-) 


M 


co o 




CN 


O 


CN| 


O 


o 


r— 


r-^ 


OS 


r~ 


CO 


OS 


CM 


CO 


sO 


OS 


CM 


sO 


ON 


m 


IN 


CO 


o 


00 




CM 


co 


o 


m 


CM 


in 


OS 


ON 


CO 


o 


CO 


CO 


o 


m 


ro 


in 


c 


CO 


T3 


C D. 


ON 


o 


O 


OS 


o 


o 


ON 


os 


os 


OS 


Os 


OS 


o 


o 


OS 


OS 


o 


o 


oo 


os 


Os 


o 


o 


ON 


o 


o 


ON 


o 


on 


O 


ON 


ON 


ON 


o 


o 


o 


CJN 


o 


o 


O 


O 


o 


■o 




cu 




















































































o 






T} 




















































































a) 


























































































u 


4J 
























































































3 


C 


Vj 


M 


o 


o 


o 


o 


o 


o 


o 


o 


O 


o 


o 


o 


o 


o 


O 


o 


o 


o 


o 


O 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


O 


O 


•U 


0) 


(1) 


4J 4-1 


CM 


-* 


00 


r^ 


r^ 


co 


CO 


in 


o 


00 


OS 


CO 


<r 


o 


OS 


IN 


o 


IN 


CM 


sO 


sO 


sO 


. — i 


<r 


. — 1 


oo 


00 


o 


in 


sO 


CO 


in 


ON 


CM 


o 


in 


IN 


IN 


CM 


CO 


sD 


ro 


4J 


JJ 


CO O 




















































































•H 


c 


M-l 


o> a 


00 


CO 


m 


OS 


<r 


-a- 


sO 


CO 


, — 1 


oo 


o 


in 


CO 


m 


CO 


IN 


o 


rN 


IN 


. — i 


I— 1 


oo 


CM 


-a- 


CO 


-a- 


m 


sO 


00 


m 


ON 


CO 


o 


CO 


o 


in 


o 


1 — 1 


sO 


CO 


CO 


o 


o 


CO 


4-1 




CM 


CNl 




CM 




CM 


CNl 


CM 




CM 




CNl 


CM 


CO 


CM 


CO 


CM 








■-H 


CM 


CNl 


CM 


CM 


CO 


CM 




CM 




CN 


CO 


CM 


CM 


CM 


CM 


CN 


CM 


CM 


CM 


S3 


o 




























































































>, 




rN 


CN 


-J" 


so 


CO 


Os 


o 


m 


CNl 


^ 


oo 


m 


in 


<f 


ON 


■a- 


. 


oo 


. 


00 


CO 


IN 


CO 


CO 


O 


CO 


00 


o 


^ H 


ON 


00 


CM 


i _ H 


^_, 


o 


sO 


-3- 


^ 


-3- 


rH 


i _ H 






4J 




CM 


vO 


<r 


i 


o 


. — 1 


sO 


r^ 


r~ 


SO 


o 


—^ 


r^ 


r- 


oo 


CO 


IN 


sO 


oo 


sO 


CM 


CO 


t-H 


o 


sO 


in 


IN 


00 


sD 


m 


t-H 


CO 


ON 


CO 


CO 


co 


in 


CO 


ON 


IN 


ON 




>s iH 


CU 






















































































H 


CO 


CJ 


sO 


n- 


-a- 


SO 


in 


CM 


CM 




CM 


OS 


ON 


-a- 


in 


-a- 


IN 


o 


o 


CO 


sO 


o 




-a- 


sO 


CO 


UN 


CO 


-3- 


CO 


OS 


CM 




-3- 


o 


m 


in 


<■ 


ON 


in 


sO 


IN 


IN 




o 


c 
<p 
-o 


a. 


OO 


On 


OS 


oo 


Os 


OS 


0> 


os 


ON 


CO 


00 


ON 


os 


Os 


00 


OS 


ON 


Ol 


00 


ON 


ON 


ON 


ON 


OS 


OS 


ON 


00 


Os 


00 


ON 


OS 


OS 


OS 


ON 


ON 


ON 


00 


ON 


ON 


ON 


ON 




-o 


0) 
























































































0) 


M 
























































































1-1 


s 


•H 


UO 


o 


o 


in 


o 


O 


m 


o 


in 


o 


in 


o 


in 


o 


m 


O 


in 


o 


m 


o 


m 


o 


in 


o 


in 


o 


m 


o 


m 


o 


m 


o 


m 


m 


in 


o 


in 


o 


in 


m 


o 




^4 


CO 


CO 


CN 


m 


m 


r^ 


o 


O 


CM 


m 


r-» 


o 


CM 


m 


IN 


o 


CM 


in 


IN 


o 


CM 


m 


IN 


o 


CM 


m 


IN 


o 


CM 


UO 


IN 


o 


CM 


m 


r- 


IN 


IN 


o 


CM 


in 


IN 


IN 


o 




D. 


en 


a. 




























~H 


























































a. 


0) 
























































































<d 


l-l 

a. 
























































































o 


























































































•H 


>s 
























































































<4-l 


4-1 




<t 


-* 


<r 


<r 


<f 


~» 


<" 


<f 


-cr 


-3- 


-a- 


-a- 


<r 


-a- 


<r 


-a- 


-a- 


-a- 


<r 


-a- 


<r 


-a- 


-a- 


Ni- 


<r 


<r 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


co 


CO 


CO 


CO 


CO 


CO 


CO 


CO 




•H 


•H 




00 


00 


00 


00 


00 


co 


oo 


00 


00 


00 


oo 


00 


oo 


oo 


oo 


00 


00 


00 


00 


00 


CO 


00 


oo 


ce 


00 


oo 


oo 


00 


CO 


00 


00 


00 


CO 


00 


co 


oo 


oo 


00 


CO 


00 


00 




u 


> 
























































































0) 


CO 




CM 


CM 


CM 


CM 


CNl 


CM 


CM 


CNl 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 




a. 


U 
























































































CO 


60 
























































































a> 


^ 






















































































rH 


u 


4J 






















































































to 


3 


c 




o 


O 


O 


O 


o 


O 


O 


o 


O 


O 


o 


o 


O 


o 


o 


O 


o 


o 


O 


O 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


•H 


4J 


01 


4-1 


CM 


<r 


CM 


r^ 


CO 


00 


co 


CM 


O 


CO 


ON 


CM 


ON 


-a- 


o 


m 


<r 


IN 


00 


sO 


sO 


o 


-■H 


IN 


•—* 


—4 


o 


00 


CO 


sO 


CO 


in 


IN 


CO 


-a- 


sO 


r- 


^H 


og 


CM 


o 


•U 


CO 


4J 


cj 




















































































•H 


•r4 


c 


a. 


oo 


CO 


00 


OS 


00 


f— 1 


SO 


sO 


i — i 


OS 


O 


r^ 


OS 


m 


m 


CM 


m 


CO 


ON 


i — I 


. — i 


o 


CM 


m 


m 


o 


sO 


-a- 


o 


in 


ON 


CO 


I— 1 


00 


CM 


CO 


O 


<r 


sO 


<r 


Os 


d 


o 


o 




1 — 1 


CN 


CM 


i — i 


CNl 


CM 


CM 


CM 


CM 


»— i 


CM 


■ — i 


CM 


CM 


CO 


CO 


CO 


CO 


. — I 


. — 1 


»—l 


CM 


CM 


CN 


CM 


CO 


CO 


CO 


CM 


CM 


-H 


CM 


CO 


CM 


CM 


CO 


CM 


CM 


CN 


CN 


CN 


M 


s 


CJ 
























































































.-< 


























































































CO 




o 


m 


nT 


r~- 


CO 


so 


CO 


in 


CNl 


CM 


00 


O 


CO 


CM 


—i 


IN 


co 


m 


CO 


CM 


m 


CO 


OS 


•a- 


m 


-a- 


sD 


-3- 


CO 


--H 


oo 


IN 


co 


CO 


-3- 


-3 


CM 


ON 


<r 


CO 


00 


<r 




1-1 


T3 


•H 


m 


in 


cn. 


m 


sD 


CM 


i— i 


CO 


i — i 


r~ 


OS 


CO 


m 


IN 


— i 


SO 


m 


OS 


-3- 


m 


<r 


IN 


-a- 


o 


m 


Os 


00 


co 


IN 


o 


CO 


rN 


<r 


m 


m 


IN 


SO 


<r 


CM 


o 


o 




4-1 


■H 


4-1 


O 


00 


00 


O 


CO 


OS 


ON 


ON 


ON 


os 


ON 


00 


00 


oo 


o 


OS 


OS 


oo 


O 


ON 


OS 


00 


00 


on 


00 


00 


O 


CO 


ON 


ON 


OS 


CO 


os 


00 


00 


00 


ON 


00 


00 


00 


00 




■H 


O 


CO 






















































































C 

M 


> 


M 


^ 






~* 






















^ 
























" 






























^H 


1 


e 




00 


in 


ON 


<t 


sO 




sO 


CO 


o 


<■ 


NT 


r-» 


in 


-a- 


o 


CO 


sO 


CO 


m 


00 


CO 


00 


CO 


CM 


sO 


oo 


sO 


CM 


CN 


SO 


CM 


•—t 


CO 


on 


<f 




CO 


00 


m 


m 


o 


CO 


iH 


o 




in 


in 


U"l 


SO 


ITI 


co 


-* 


sO 


r-- 


oo 


-* 


m 


SO 


oo 


OS 


OS 


^H 


CM 


CO 


•a- 


sO 


oo 


-a- 


in 


UN 


oo 


ON 


SO 


sO 


ON 


•a- 


m 


CO 


IN 


m 


OS 


-a- 


<r 


00 


m 


IN 


•H 


O 


•H 


c 


o 


O 


o 


o 


o 


o 


O 


O 


o 


o 


O 


o 


O 


o 


O 


o 


. 1 


•— 1 


o 


o 


o 


o 


o 


O 


o 


o 


O 


o 


O 


O 


o 


o 


o 


o 


O 


o 


o 


o 


o 


o 


o 


44 


en 


4-1 


•H 




















































































•H 


c 


CO 




o 


1 


1 


1 


1 


1 


1 


1 


t 


1 


1 


i 


1 


i 


1 


1 


1 


1 


i 


i 


1 


1 


■ 


1 


i 


1 


1 


1 


1 


1 


i 


i 


1 


1 


I 


1 


i 


i 


1 


i 


1 


C 


o 


T3 




1 


















































































H 


CJ 




























































































0) 

cx 




























































































oo 


OS 


o 


_l 


CM 


CO 


<r 


in 


sO 


r^ 


00 


OS 


o 


^ 


CM 


CO 


-a- 


m 


sO 


IN 


CO 


ON 


o 


_, 


CM 


CO 


<r 


in 


sO 


IN 


oo 


ON 


o 


— < 


CM 


CO 


-a- 


m 


sO 


IN 


00 






e 




so 


sO 


r^- 


r^ 


r-~ 


p^ 


p-^ 


r^ 


p~ 


i — 


p^ 


r^ 


00 


00 


00 


CO 


00 


oo 


oo 


00 


CO 


00 


OS 


OS 


OS 


ON 


OS 


ON 


ON 


ON 


OS 


ON 


c 


o 


o 


o 


o 


o 


o 


o 


o 






a) 

CO 




































































CM 


CM 


CM 


CM 


CM 


CM 


CN 


CM 


^4 



23 



o 



00 

m 



o 
o 



CJN 

o 



nO 
CM 
st 



ON 


p^ 


_ 


NO 


co 


co 


pi 


r^ 


ON 


ON 


1 


p^ 


in 


in 


ao 


o 


O 


m 


CM 


NO 


ON 


CM 


r~ 


ON 


^ H 


m 


co 


CO 


in 


o 


CO 


O 


oo 


ao 


CM 


, 


«4t 


co 


co 


CO 


NO 


^o 


oo r-. 


U"N 


cs 


DO 


□ 


-j 


m 


BO 


c 


p^ 


sr 


in 


— * 


— 


cm 


CO 


r> 


CO 


00 


CM 


""< 


CM 


00 


O 


CO 


ON 


oo 


00 


in 


O 


st 


r- 


o 


O 


ON 


co 


CO 


CM 


m 


nC 


o 


in 


NO 


co -3 


CM 


_ 


On 


U-N 


co 


p** 


in 


X 


IT 


CM 


-3 


_l 


_ 


o 


CM 


m 


r~ 


XT 


NO 


on 


r~- 


ON 


go 


m 


\o 


00 


co 


CM 


m 


_, 


O 


co 


ON 


o 


o 


-3 


ON 


CM 


o 


CO 


NO 


CO 


00 co 


O 


a 


ON 




o 










CM 




CM. 








CM 










CM 






CM 






O 






CM 


CM 






CM 


CM 


CM 




CM 


CM 


CM 








■3 


go 


ON 


On 


rsi 


-3 


O 


ao 


ON 


r^ 




<- 


CO 


r*. 


p^ 


NO 


o 




«3 


<r 


NO 


CM 


NO 


o 


00 


o 


cm 


^O 


p~. 


CM 


O 


SO 


o 


st 


-3 






r^ 


ST 


st 


st 


NO 


NO ON 


-3 


r-. 


c 


r-* 


co 


~3 


in 


— 


-3- 


NO 


CM 


-» 


X 


in 


CM 


ON 


o» 


o 


<f 


co 


r-* 


ON 


a 


CO 


ON 


NO 


nO 


ON 


CM 


in 


— ' 


CO 


o 


•"• 


oo 


CMJ 


ON 


m 


CO 


O 


00 


O 


r-~ cm 


cm 


p*l 


-3 


_ 


ON 


CM 


NO 


_ 


_ 


co 


ON 


CM 


-3 


CO 


_, 


CM 


_, 


cm 


o 


Q 


co 


_, 


co 


nO 


CO 


NO 


ON 


O 


^ 


sr 


ON 


co 


r-» 


oo 


ON 


ON 


NO 


or 


O 


on 


ON 


CO 


in on 


N 


"* 


NO 


co 


" 


CM. 


CO 


-3 


NO 


r-^ 


Pn! 


cm 


-3 


NO 


00 


CM 


>3 


ie 


vo 


P"* 


ON 


CM 


CO 


in 


r^ 


CM 


CO 


MD 


00 


CM 


CO 


in 


CO 


r-~ 


^ H 


CM 


SI 


r^ 


r~ 


oo 


■"* 


CO 


in no 


_ 


ON 


ON 


~3 





-3 


p^ 


CM 


p*. 


l — 


00 


X 


go 


X 


, 


O 


O 


o 


t 


CO 


o 


NO 


^r 


O 


O 


ON 


r> 


CO 


<r 


O 


h- 


O 


O 


<r 


O 


O 


O 


sr 


CO 


oo 


o 


o 


r- O 


O 


>C 


X 


ON 


o 


NO 


CM 


DO 


r** 


-3 


1 — 


— 


X 


cri 


NO 


oo 


NO 


o 


iC 


1 — 


O 


st 


CM 


o 


o 


o 


1-1 


<r 


co 


o 


m 


CM 


O 


ON 


o 


in 


o 


m 


o 


NO 


o 


o 


NO O 


in 


sC 


r^ 


P*~ 


o 


nO 


X 


in 


in 


00 


CM 


DO 


i — . 


m 


NO 


ON 


CM 


o 


CO 


Ol 


O 


ON 


<r 


o 


o 


<3- 


O 


r*s 


ao 


o 


c^ 


H 


o 


r^ 


o 


_! 


r^ 


CM 


m 


ON 


o 


O 


r- O 


in 


^ 


rN 


00 


o 


X 


ON 


X 


p-~ 


oo 


NO 


ON 


i — 


p^ 


NO 


ON 


ON 


o 


00 


XI 


o 


ao 


ON 


o 


o 


p^ 


in 


NO 


00 


o 


ON 


00 


o 


ON 


o 


ON 


o 


ON 


CO 


00 


o 


Q 


ON O 


•3 


-. 




-3- 


CO 


CS 




- 


CO 


ON 


o 


NO 


ON 


m 


CO 


On 


CO 


_ 


r*» 


ON 


1 — 


oo 


oo 


o 


ON 


00 


•* 


•* 


NO 


ON 


CO 


<r 


NO 


o 


ON 




ON 


CM 


CTN 




on 


r» 


O O 


r*» 


«n 


ON 


— ' 


cn 


ON 


CM 


~3 


on 


CO 


CO 


CM 


~ " 


m 


ON 


in 


ON 


NO 


CO 


<r 


ON 


""" 


m 


^r 


m 


CM 


O 


*"• 


oo 


ON 


r^ 


XI 


NO 


ON 


ON 


~ ' 


r-* 


ON 


CO 


oo 


oo 


CO 


m -3 



r^ ao o c* o* -^ 



o o o o 

— (■»>. ^ C 



o o o o o o 

O n fO O (N ^ 



— m 

CM —• 


a 


00 
CM 


CO 

co 


in 

CM 


CO 


-3 


CO 
CM 


CO 
CM 


NO 


CM 
CO 


CO 
CM 


B" 


CM 


00 
CM 


m 


~3 
CM 


CM 


CJ 


CM 


00 
CM 


m 
CM 


NO 

CM 


ON 
CM 


CM 


P^ 


CM 


m 

CM 


-3 
CM 


CM 


ON 
CM 


NO 

CM 


r-. 
CM 


O -3 
CO CM 


CM 


CM CO 
CM CM 


CO 
CM 


CO 


co 


O 

CO 


CO 


^^ CO 

!■*» in 


CO 


o> 
ao 


CM 

m 


X 
X 


X 


NO 


CO 


00 

m 


CM 


CM 

in 


o 

c 


0" 


O 

in 


m 


co 


NO 


in 


X' 
nO 


CM 

CO 


ON 

CO 


CO 


O 

NO 


00 
CM 


CM 
CM 


NO 

O 


CO 


in 


o 

CM 


X) 
X 


CM 


co 


NO 

ON 


CM CO 
ON CO 


o 
to 


00 00 
P^ NO 


NO 

-3 


p^ 


X> 


CJ 


ON 

CM 



OC 00 ^ oo 



\r\ o it* O 
eg m r^ O 



u. iri o O ^ o 
N N ia in fN. o 



in iAO m O 
in N in n o 



in o ia in o o 

(N lAN N OO 



m o m o 
cm in r- o 



c~ 


co 


-- 


CO 


CO 


co 


CO 


CO 


CO 


CN 


~3 ~3 


n9J 


-3 


sT 


<T 


-r 


-3 


-3 


-3 


-3 


-3 


<t 


-3 


-3 


-3 


<* 


<r 


■3 


-3 


•3 


•* 


s» 


-3 


CO CO 


CO 


CO CO 


CO 


CO CO 


CO CO 


X 


X 


-' 


00 


00 


DC 


OC 


X 


X 


CO 


an on 


X 


go 


on 


an 


00 


X 


Tj 


go 


00 


on 


00 


rfj 


00 


00 


CO' 


CO 


00 


ao 


x. 


CO 


CC- 


00 


oo oo 


CO 


oo on 


on 


00 00 


oo oo 






CM 


CM 


CM 


-. 


CM 


CM 


CM 


CM 


CM CM 


CM 


CM 


CM 


CM 


CM 


'1 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CJ 


CM 


CM 


CM 


CM 


CJ 


CM 


CM CM 


CM 


CM CM 


CM 


CM CM 


CM CM 



- 


o 


— 


o 


o 


o 


— 


o 


o 


o 


O 


O 


c 


a 


o 


o 


o 


o 


o 


o 


o 


o o 


O 


O 


O 


o 


O 


o 


o 


o 


o 


o 


O 


o o 


o 


o o 


O 


o 


o 


o 


O 


"" " 


X 


X 


o 


CM 


B 


- 


r^ 


X. 


CM 


oo 


-r 


c 


r~- 


m 


NO 


-* 


PN» 


NO 


CM 


00 


CO CM 


in 


-3 


O 


ON 


00 


o 


r^ 


P-. 


in 


ON 


ON 


O NO 


CO 


CM CO 


NO 


rt 


00 


r* 


•"' 


_ 


~c 




o 


O 




m 


nO 


CO 


<T 


p^ 


CM 


NO 


■3 


_ 


co 


CM 


CM 


r^ 


CO 


ON 


00 ON 


9 


NO 


_ 


p^ 


_^ 


ON 


ON 


r> 


T 


in 


ON 


-3 -3 


m 


m ~3 


•3 


_, 


CM 


c 1 


_ 


CM 


"" 


" 


CO 


•* 




CO 




CM 


CM 




CO 


CM 


'J 


CM 


CM 


CO 


CO 


CM 


CM 


CM 


CM CM 


CM 


CO 


CM 


•"* 


CM 


CM 


CM 


cl 


CM 


CO 


CM 


CO CM 


CO 


CM CM 


CM 


-3 


•* 


to 


-.f 


.- 


X. 


■£> 


m 


M3 




on 


p* 


ON 


-3 


in 


^ 


O 


CO 


P~ 


-3- 


IT 


-3 


h* 


en 


CO 


00 O 


o 


-3 


in 


CO 


x. 


CM 


-3 


a\ 


CM 


r^ 


P-~ 


CM —i 


St 


— 1 ON 


nO 


CM 


-r 


r s 


PN* 


X 


KM 


.' 


nO 


-3 


K 


*M 


nO 


00 


r*. 


O 


co 


r^ 


CM 


— - 


^H 


00 


m 


CO 


ON 


CO 


ON 00 


00 


nO 


o 


H 


— 1 


CO 


CM 


o 


CI 


P~ 


NO 


CM NO 


at 


r~ o 


f^- 


ON 


ro 


St 


^T 


o 


o 


o> 


o< 


~ 


BC 


B 


00 


X 


p-. 


ao 


ON 


■y 


ON 


ON 


oo 


a 


X. 


ON 


X 


p^ 


00 00 


r~ 


On 


00 


O 


en 


ON 


00 


00 


O 


00 


oo 


on r^ 


CO 


p~ oo 


P^ 


ON 


o 


CI. 


o 


■"• 


— 






— 




— ■ 






































— ■ 










"- , 
















■"■ 




-• 



c <r oc o 

' ■& CM 

COO — 



CO "^ p^ On ^3 MD 

— in CM -3 -o o 

— o — o o — 



O On -3 -3 m 

st in p- p^ no 
O O O O O 



co r^. on in cm —i 
~3 on in \0 '-' nO 
o o o o — o 



on — < in o 
co p^ in cm 
O O O — 



on co p-^. in 

St 00 P— CM 

o o o — 



p^ st no on on 
~t ON cm ao CM 

O O —i o — 



cm p~ in oo no o 
no cm no in st no 
o o o o o o 



no -3 in st 
-3 CO — i O 

H.HHN 

till 



cr C — "i 



•J ^ C p» 00 
^J - i -I N CM 



ON O — • CM CO 
— ' I N (N| N 
CM CM CM CM CM 



-3 in mo p* oo on 

CM CM CM CM CM CM 
CM CM CM CM CM CM 



O — ■ CM CO 
CO CO CO CO 
CM CM CM CM 



~3 in \D r^ 

CO CO CO CO 
CM CM CM CM 



on on o — < cm 

CO CO -3 -3 -3 
CM CM CM CM CM 



co -t m no r~ on 

>» -3 -3 >» st -3 
CM CM CM CM CM CM 



ON O — < CM 

st in in m 

CM CM CM CM 



24 



0) 

3 

d 



c 
o 
o 
I 



>N 

14 
o 

4-1 

« 

o 
.o 






c 
o 
1-1 1-1 

CD CD 
CD P. 

O 




-3 
o 

NO 


ON 
O 


o 

ON 

oo 


NO 
NO 

CM 




oo 

-3 
-3 


-3 
fv 

-3 


NO 


in 

CO 


Internal 

friction 

angle , 

deg 


in 
in 

NO 
CO 


00 

m 

-3 
CO 


ON 
NO 

rv 

CO 


ON 

rv 

ON 
CO 




m 

CO 

o 

-3 


ON 
r- 

oo 

CO 


in 
-3 


-3 

in 

in 

CO 


Fellenius 

factor of 

safety 


> 1.775 


i 1.028 


> 2.159 


r- 

CO 

in 

*—* 




> 1.642 


> 1.736 


> 1.395 


> 1.006 


Wet 

density, 

pcf 


CM vO ON O O O 

«o -3 -3 -3 co -3 

oicocn ho o 

HrfN NHCM 


118.89 
111.92 
121.95 
118.50 


122.95 
123.18 
116.91 
119.78 


99.72 
103.75 
110.84 
104.83 


-3 O 
O CM 

CO -3 

•— i *— i 

^H f— 1 


111.80 
105.53 
105.73 
115.56 


112.62 
113.51 
118.58 
119.86 
120.32 


95.78 

88.96 

111.76 

114.20 

120.94 


111.80 
106.50 
110.64 
100.07 
108.16 


Peak 

stress, 

psi 


rv cm cm r- co on 
rv in cm in co ~h 

o -3 cm co m on 
co cm -3 no on rv 


18.27 
35.97 
52.11 
70.34 


rv co — < in 

*-" -3 CM ON 

CON MO 
CM -3 NO 00 


24.00 
43.78 
52.11 
64.61 


O tv 
ON -3 

— 1 NO 

r- oo 


oo rv on oo 
o -3 o no 

NO 00 -3 ^ 
CM -3 NO ON 


cm on so in in 
m co -a- o on 

-3 no co co in 

CM -3- |v vO 00 


O rv *-t co -3- 
O 00 CM — I no 

-3 in rv co o 
CM -3 nO O ON 

t—i 


ON CM 00 -3 O 
r— o cm o on 

CON vO CO h 

-h co in con 


Initial 
satura- 
tion, 
pet 


m rv o o o oo 

O ON O O ON NO 

co cm o o oo rv 

00 00 O O 00 00 

•— » .—i 


91.90 
100.00 
100.00 

91.28 


100.00 

100.00 

88.67 

83.10 


vO ^h O CM O vO 

r-*. r^ o u"i O r->* 

ON ~* O O O vt 

P*ivO O lAO vO 


O ON CO CM 

ON CO -J rf 

oo on m m 

m -3 -3 NO 


OO 00 -3 ON no 
ON •— i 00 CO On 

rv o no cm oo 

^ON IN DON 


no oo -3 r> m 

ON 00 O ON ON 

— i o cm <■ rv 
co cm no no rv 


— i no no rv o 
no on rv on r-- 

oo o no m on 
i — no no co in 


Consoli- 
dated 
dry 
density, 


o 


r- •* co-* on 

OONNvOCOH 

CM IV CO CM r-< CO 
O ON O O O O 

•—i .-H t— J r— ) —4 


98.81 

103.21 

98.25 

101.01 


101.73 
103.02 
100.10 
101.83 


92.36 
91.58 
93.51 
96.83 


CM —I 
NO CM 

O CM 
O O 

•— 1 F-H 


~h oo in no 
no r~ -3 on 

00 NO ON -3 

ON ON ON O 


ONl/N in H N 
IN H VO CO 1 — . 

|v ON -3 in -3 
ON ON o o o 


p- o m o -3 

NO O ON 00 NO 

cm co on h in 
On ON ON o o 


N- CM CO ON CM 
CM CO ON CM -3 

CM CM I-. NO NO 
ON ON ON ON ON 


Moisture 
content 

after 

test, 


4J 
CJ 


o o o o o o 
rv no oo on o oo 

.— i in in -a- no co 

CM CM CM CM CM CM 


o o o o 
in rv on m 

O -3" -H o 

CO CO CO CO 


o o o o 

NO CO CM no 

-3 -3- CO -3 
CM CM CM CM 


o o o o o o 
m in co co oo in 

-3 -3 00 1 — CM ON 

hniOhio h 


o o o o 

— i O 00 ON 
00 no -3 00 


o o o o o 
~h in in cm co 

HO N-IN 
CM CM CM CM CM 


o o o o o 

— 1 CM NO NO -3 

CM 00 ON ON — < 

— 1 —1 -H CM 


o o o o o 

ON CM -3 nO in 

00 CM CM CM O 
CM CM CM H CM 


Dry 

density, 

pcf 


oiNNOom 

CM CO — 1 CM — I CM 

CO •* 00 N CO N 
ON ON ON ON ON ON 


91.10 
83.09 
94.45 
90.81 


00 O O CO 
NO *H ON «— 1 

00 ON -3 nO 

ON ON 91 ON 


O co -3 rv 

^H CO -^ CO 

MOOON 
00 00 OO 00 


CM tv 

— i m 
m in 

00 ON 


rv oo O on 

VO ON HH 

-3 O CM P- 

ON ON ON ON 


ON O O ON 00 
ON CM 00 00 CO 

CM -3 NO 00 CO 

ON ON ON ON ON 


-3- CM m ON CM 
-3 CM -3 -3 no 

in cm co in on 

00 00 ON ON ON 


-3 in on r-- no 
r- — i co oo r- 

nO r-. o oo on 
00 00 ON 00 00 


Applied 
pressure, 

psi 


in in o m o o 
cm cm m rv o o 

i— i f— i 


in o in o 
cm in tv o 


m o m o 
cm m r- o 


m o in m 

Nm m — 


o o 
o o 

~H i— 1 


m o m o 
cm in rv o 


in o in in o 
cm in rv rv o 


m o m o o 
cm in iv o o 


in o m o o 
cm m i-. o o 


o 

1-1 >N 
■4-1 4-> 
1-1 iH 

o > 

V CO 

a, u 

C/3 00 


CO CO CO CO CO CO 

oo oo oo oo oo oo 

CM CM CM CM CM CM 


CO CO CO CO 

oo oo oo oo 

CM CM CM CM 


CO CO CO CO 
00 00 00 00 

CM CM CM CM 


-3 -3- -3 -3 
00 00 00 00 

CM CM CM CM 


-3 -3 
00 00 

CM CM 


-3-3-3-3 
00 00 00 00 

CM CM CM CM 


-3-3-3-3-3 

oo oo oo oo oo 

CM CM CM CM CM 


-3-3-3-3-3 
00 00 00 00 00 

CM CM CM CM CM 


-3-3-3-3-3 
00 00 00 00 00 

CM CM CM CM CM 


Initial 

moisture 

content, 

pet 


O O O O O O 

-3 no in oo cm co 


O O O O 

in o co in 


O O O O 
rv 00 O no 


O O O O 

in m cm m 


O O 

— i m 


O O O O 

— i m oo on 


O O O O O 

i-~- oo m o co 


o o o o o 

^H in nO no -3 


o o o o o 
on cm no no in 


co in on — • oo in 

CM CM CM CO CM CM 


O CM -* o 

CO -3" CO CO 


oo o rv -3 

CM CO CM CM 


-3 -3 -3 rv 

HN-J -H 


— 1 ON 
-3 —l 


00 NO -3 00 


-h ^H CM CO CM 
CM CM CM CM CM 


CM 00 ON ON -H 
—i — l — I CM 


00 CM CM CM O 
CM CM CM -* CM 


Initial 
void 
ratio 


rv co o oo oo rv 
JN rv o ~H ON *-< 
rv oo oo oo oo oo 


ON NO ~H \0 

CO CM —I -* 
ON t— 1 ON ON 


O CO CM 00 
ON 00 NO CO 

rv r-. oo oo 


NO 00 CM -3 

CON -n 00 
OHCMOV 


co m 
oo m 
o 00 


co on m -3 

P- -3 CM CM 

oo on on oo 


NO CM CM CO CM 

O 00 CO ON o 

ON 00 00 in 00 


in no rv i — o 
r-. in on in oo 

oi cocoin 


-3 -3 -h in in 
-3 co no on r-. 

O O ON ON ON 


o 


•— 1 




t— l »— i i— i 


•— i 






~H ~H 


~* f— 1 


Initial 
consoli- 
dation, 
in 


(i» 1 — Ch CO H N 

■o co -3 in oo m 
o o o o o o 


oo in on — i 
rv on m o 

o ■— l o •— i 


O 00 CM NO 

co co in m 
o o o o 


n o co rv 
in on -3 rv 
o o ^ o 


■3 m 

in no 
-i O 


O O -3 -3 

-3 no rv rv 
o o o o 


OlOlOHH 

<r in iv no so 
o o o o o 


oo no m cm r- 
r— — i vo no m 
o — i o o o 


o no r- r- on 
no m r-- o- no 
o o o o o 


O 1 1 1 1 1 l 1 1 l till l l l l l i l l l i i i i i i i i i i i i i i i i 


01 

.-1 

i" 

CO 
GO 




■o ■* in vo iv co 
n in in m in in 

M CM CM CM CM CM 


CHO-HN 

in no no no 

CM CM CM CM 


co -3 m vo 

NO NO NO NO 

CM CM CM CM 


NOOONOH CM 
O^O »ONN N 
CM CM CM CM CM CM 


co -3 m no 

r^ n inn 

CM CM CM CM 


NCO ONOH 
M^NOOCO 
CM CM CM CM CM 


CM CO -3 in nO 

OO 00 00 00 00 
CM CM CM CM CM 


IV 00 ON O — 1 
00 00 00 ON ON 
CM CM CM CM CM 



25 















CO 
































co 


































- 








hN 






on 






O 
















en 










C_N 








NO 




CM 








vO 








in 






~3 






© 






o 








X' 










O 








ON 




ON 




















































































cm 
















<T 






in 






o 


















m 








CO 




CM 








ON 








-3 






on 






O 






NO 








<r 










CM 








o 




ON 








co 








CM 






on 






CO 






CO 








00 










CO 








ON 




ON 








r- 








vD 






-3 






in 






00 








r~- 










NO 








~3 




rv 








rN 








^N 






CO 






CO 






CO 








CO 










CO 








CO 




CO 








r-» 








o 






<r 






CM 






CO 








in 










O 








in 




ON 








-3 








NO 






in 






an 
















CO 










CM 








NO 




00 








-3 








© 






-3 






in 






r*- 








f-H 










NO 








-3 




■<T 








~* 










































' 










~* 




















on 


^ 


go 


in 


ao 


I — 


© 


CO 


-3 


ON 


, 


, 


. 


ro 


a 


CM 


ON 


r» 


CM 


m 


NO 


On 


ON 


vO 


CM 


ON 


r^ 


r^ 


m 


ON 


NO 


-3 


_, 


r^ 


r^ 


ON h- 


ON 


CM 


nO 


On 


X 


in 


nO 


nO 


o 


in 


CM 


CM 


NO 


on 


rv 


ro 


X 


CM 


NO 


NO 


ON 


"■' 


— ' 


— ' 


o 


CM 


o 


-3 


— I 


~> 


ON 


r>. 


oo 


CM 


ci 


O 


"* 


O -> 


r^ 


O 


vC 


90 


CSI 


-3 


vO 


in 


X 


r*. 


ON 


ON 


in 


NO 


ON 


CM 


CM 


r*. 


P^- 


in 


r^> 


r~ 


ON 


CM 


o 


CM 


CM 


CO 


^ 


—, 


_< 


_i 


© 


ON 


CO 


00 


_ 


H — ■ 


^i 


_ 




















o 


3 




o 


CM 


CM 
















CM 


CM 


CM 


CM 


CM 


O) 


CM 


CM 


CM 








CM 


CM CM 


CM 


CM 


lO 


90 






ON 


p~ 


o 


DO 


o 


o 


NO 


X 


o 


M3 


r^ 


«* 


nD 


ON 


~o 


-3 




-3 


x> 


NO 


CM 


ON 


nO 


CM 


-3 


■3- 


•3- 


O 


o 


NO 


00 


-3 CM 


NO 


r» 


CT* 


in 


0* 


CN 


— 


CM 


in 


X 


ON 


~3 


NO 


CM 


m 


ON 


X 


X 


o 


r- 


— < 


CM 


r^ 


an 


"-< 


—> 


CO 


— ' 


ON 


CM 


CM 


n3 


1-1 


-3 


-* 


r~ 


ON 


-3- CM 


ON 


CM 


rsi 


90 


a 


-^ 


on 


on 


vO 


00 


— 


__ 


a 


NO 


-3 


CM 


in 


i — 


NO 


00 


© 


in 


ON 


on 


_, 


ro 


,-^ 


ON 


CM 


CM 


m 


o 


on 


_ 


ON 


m 


CO 


CM CM 


o 


_H 


-. 


ro 


>c 


vO 


'"* 


™ 


co 


in 


r-. 


CM 


<r 


in 


r — 


CM 


■» 


m 


r*- 


1 ' 


«3 


m 


r^ 


"* 


<r 


in 


in 


Pv 


CM 


<r 


m 


NO 


r-* 


CM 


cn 


l/N 


r^ 


CM «3 


NO 


CO 


on 


O 


_. 


X 


ro 


o 


© 


ON 


O 


CM 


O 


m 


CO 


o 


o 


00 


ON 


-3 


NO 


CM 


ro 


ro 


sO 


O 


CO 


CO 


rv 


rN 


© 


O 


o 


CM 


o 


© 


ON 


*H CM 


o 


O 


ro 


3 


r 


ON 


CM 


o 


r 


nO 


O 


CO 


in 


in 


p^ 


o 


o 


3 


CO 


— ' 


-3- 


CO 


<r 


O 


«* 


CM 


00 


On 


rs 


CO 


o 


O 


o 


CO 


CO 


o 


in 


rv co 


o 


O 


90 


- 


3 


in 


nO 


o 


o 


r^ 


© 


rv 


in 


r-» 


CM 


o 


a 


Csl 


<3 


CO 


-T 


— 


oo 


ON 


CM 


L/V 


NO 


rv 


ON 


—, 


o 


o 


o 


ON 


o- 


o 


on 


H -3- 


o 


o 


CT> 


3 




00 


0> 


o 


o 


on 


o 


*"* 


nO 


X 


00 


o 


o 


■X 


ON 


on 


ON 


ON 


00 


NO 


ON 


ON 


oo 


00 


ON 


ON 


O 


C_N 


o 


00 


CTN 


o 


on 


ON ON 


O 


O 


DO 


-3 


ro 


o 


ro 


o 


•* 




in 


r-v 


CO 


CO 


r- 


m 


CO 






NO 


r~ 


lO 


_ 




ON 




ON 


00 


rv 


CM 


ON 


«3 


00 


in 


MD 


<r 


r*^ 


ON -* 


NO 


CM 


co 


O 


O 


- 


NO 


o 


ON 


CM 


nO 


NO 


CM 


— ' 


CM 


CM 


CO 


o 


ON 


m 


a 


-* 


CM 


— ' 


CO 


m 


DO 


oo 


in 


m 


CO 


o 


CM 


NO 


m 


on 


ro 


oo r-v 


- 1 


-7 


on 


90 


in 




rv 


on 


CO 


CO 


ON 


CM 


CO 


_ 


in 


ON 


_ 


_ 


m 


ON 


co 


<%J 


00 


r^ 


<J- 


CO 


r*» 


© 


-3 


DO 


sD 


ON 


ON 


o 


rH 


CM 


O 


CM NO 


ON 


ON 


90 


o> 


3 


3 


O 


ON 


© 


© 


© 


ON 


On 


C 


on 


ON O 


© 


o 


ON 


O 


o 


o 


ON 


o 


c 


© 


r^ 


O 


O 


O 


o 


o 


o 


o 


o 


^ 


O O 


o 


O 








































CM 






































O 


O 


O 


o 


O 


o 


o 


© 


O 


o 


© 


© 


o 


o 


o 


o 


o 


o 


o 


© 


o 


o 


o 


O 


O 


o 


O 


© 


o 


Q 


o 


o 


o 


o 


O 


O O 


o 


o 


o 


O 


in 


-. 


00 


f*N 


3 


I**. 


o 


-3 


3 


ON 


ON 


CM 


ON 


NO 


r^ 


CM 


ON 


lO 


ON 


ON 


r— 


m 


<r 


CM 


-3- 


ON 


m 


00 


-3 


r^ 


ON 


ON 


in 


CM r^ 


DO 


■* 


X 


r* 


CM 


_ 


nO 


__ 


ON 


CTn 


ON 


NO 


r, 


ON 


CO 


r*. 


lO 


in 


NO 


in 


-3 


o 


CM 


CM 


CO 


■* 


CM 


CO 


ro 


-^ 


ON 


<r 


m 


NO 


NO 


ON 


CO 


in co 


<r 


m 


r-i 


n 


rM 


ro 


CM 


CO 


CM 


CM 


CM 


CM 


CM 


CM 


CO 


CM 


CM 


r-: 


CM 


CM 


CM 


en 


CM 


CM 


CM 


CM 


r~j 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM CM 


CM 


CM 


iTt 


co 






CM 


<-> 


^ 


CN 


CO 


NO 


, 


O 


<3 


r- 


r^ 


CO 


ON 


on 


. 


o 


NO 


ON 


x> 


O 


ON 


<f 


on 


O 


r~ 


ON 


00 


_, 


rN 


O 


_, 


CM NO 


ON 


o 


in 


-. 


CI 


ro 


o 


— ■ 


-3 


nO 


-3 


-3 


3 


3 


ON 


— ' 


r— 


CO 


ao 


CO 


<r 


r^ 


ON 


CM 


o 


CM 


Ifi 


CM 


— ' 


-3 


~+ 


m 


ro 


"* 


CM 


ON 


■"• 


rv ON 


m 


hi 


-3 


— 


o 


r-» 


CM 


oo 


_« 


~ 


CM 


NO 


X 


a 


_, 


NO 


NO 


CO 


CM 


CM 


-3 


ON 


NO 


_ 


r* 


X! 


ON 


O 


an 


ON 


<t 


r^ 


NO 


<t 


CO 


o 


00 


nO Pv 


rv 


NO 


X 


on 




X 


On 


ao 


ON 


ON 


ON 


00 


X 


ON 


00 


ON 


■y 


ON 


o> 


ON 


ON 


X 


ON 


ON 


Oi 


ON 


ON 


o 


ON 


ON 


ON 


ON 


ON 


ON 


ON 


ON 


ON 


ON On 


ON 


ON 


.- 


o 


in 


o 


O 


in 


o 


in 


o 


in 


o 


m 


© 


m o 


in 


o 


m 


© 


u-, 


o 


in 


© 


m 


m 


o 


m 


O 


m 


m 


o 


in 


o 


m 


o 


in o 


m 


o 


-. 


m 


r^ 


= 


c 


CM 


in 


r* 


O 


CM 


1/1 


r-- 


o 


CM 


m 


r-- 


o 


CM 


m 


r^ 


o 


CM 


in 


r* 




o 


CM 


m 


r^ 


r-. 


o 


CM 


m 


r*. 


o 


cm m 


r^ 


o 


-7 


- 


-3 


- 


<T 


•iT 


-3 


«3 


~3 


-3 


-3- 


~3 


-3 


-3 


-3 


-3 


-3 


<r 


-3 


-T 


<t 


~3 


-T 


•* 


-* 


-3 


-3 


-3 


^ , 


-* 


■J- 


-<r 


-3 


•* 


-3 


-3 -3 


<r 


-T 


x 


X 


X 


X 


ao 


00 


X 


X 


ao 


00 


X 


X 


oo 


00 


DO 


X 


oo 


00 


X 


X 


00 


an 


X 


00 


x. 


an 


00 


» 


X) 


X) 


an 


on 


00 


00 


00 


on an 


X' 


CO 






CM 


- 1 


CM 


CM 


-1 


- 1 


CM 


CM 


CM 


CN 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM CM 


CM 


C 1 


O 


a 


o 




o 


o 


O 


© 


O 


o 


o 


O 


© 


© 


O 


o 


o 


o 


© 


© 


o 


o 


o 


o 


o 


o 


o 


O 


o 


o 


o 


o 


o 


o 


O 


o o 


O 


O 


o 


.- 


- 


CM 


■* 


— 


nO 


ON 


© 


NO 


-r 


ON 


ON 


CO 


in 


O 


CM 


ON 


CM 


-3 


00 


ON 


ON 


O 


X 


on 


CO 


CM 


10 


CI 


o 


oo 


~* 


m 


CO 


ON ON 


CM 


ON 


■ 


m 


■ 


__ 


_ 


ON 


in 




in 


on 


e»i 


ON 


CO 


CO 


9 


nO 


O 


NO 


ON 


_ 


in 


CM 


NO 


r^ 


CI 


ro 


on 


in 


CI 


91 


—. 


r-. 


a 


-1- 


oo 


NO NO 


ON 


C--1 


— 


— 


-i 


ro 


en 


en 


CO 


— 


CO 


CM 






CO 


ro 


CM 


CM 


CO 


CM 


CM 


ro 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CM 


CO 


CM 


ro 


CM 


m 


CO 


CM 


CM CM 


CI 


en 


l*» 


- ; 


DO 


. 


i — 


CM 


X. 


NO 


00 


. 


in 


o 


-3 


CO 


CM 


o 


ON 


ON 


DO 


r^ 


ON 


CM 


NO 


m 


00 


Oi 


NO 


-3 


CO 


r^ 


O 


~3 


Cl 


m 


r*. 


CO O 


r— 


r- 


o- 


O 


-O 


ro 


CM 


— ■ 


ro 


m 




in 


— . 


r*» 


nO 


>3 


CO 


o 


© 


—i 


fNN- 


rNi 


CM 


-3 


C i 


O 


r-~ 


nO 


o 


X) 


ao 


— i 


-3 


on 


O 


o 


O 


CO -- 


»H 


c^ 


c 


CH 


p* 


O 


ON 


O 


ON 


on 


ON 


O 


C 


ON 


— 


ao 


DO 


ON 


ON 


ON 


90 


ON 


an 


ON 


oo 


X 


r^. 


r^ 


on 


p*l 


00 


X 


an 


on 


en 


on 


an 


oo on 


Xj 


CO 


w * 






— 




— 








— ' 


-* 




•" 




















































- 


CM 


.- 


- 


in 




a 


' I 


r- 


r-» 


c 


o 


© 




m 


nO 


CO 


CM 


-3 


'J 


-3 


o 


o 


m 


e 


-£> 




• 


ON 


m 


00 


in 


CM 


r- 




O CM 


e 


00 


r 


- 


-3 


- 


<3 


a 


f : 


- 1 


LT 


nO 


j~ 


m— 


-3 


CO 


T 


r^ 


CM 


r^ 


90 


CM 


© 


c 


r^ 


9 


r^. 


ON 


vO 


oo 


— 1 


o 


—t 


a 


x> 


^H 


~* 


no an 


o 


— i 




□ 


a 


i 


i 




' 


i 


1 


o 

1 


a 
i 


' 


' 


O 


a 


© 
1 


1 


© 


c 


' 


' 


o 

1 


O 
l 


o 

1 


o 

1 


o 

1 


o 

i 


O 
I 


1 


' 


i 


O 

i 


O 
i 


' 


i 


o o 
■ i 


i 


i 




— 


- 


.' 


o 


r^ 


DO 


i 


© 




'j 


c 


-3 


m 


e 


h* 


X 


ON 


o 




•vi 


ro 


I 


m 


sO 


rs 


00 


a 


o 




CM 


ro 


-3 


m 


nO 


r~ 00 


o- 


a 


9 


~ 


- 


o» 


T 


ON 


0> 


ON 


© 


a 


a 


o 


o 


o o 


o 


© 


o 






















CM 


CM 


CM 


CM 


CM 


Cm 


CM 


CM CM 


CM 


en 


EN 








CM 


CM 


' 1 


' i 


CO 


ro 


— 


" 


CO 


ro 


CO 


" 


m 


CO 


"N 


CO 


CO 


CO 


CO 


m 


ro 


ro 


ro 


CO 


en 


ro 


CO 


CO 


CO 


ro 


CO 


ro ro 


ro 


en 



26 



TABLE A-2. - SW Laboratory data 





Fellenius 


Wet 


Internal 


Cohesion, 




Fellenius 


Wet 


Internal 


Cohesion, 


Sample 


factor of 


density, 


friction 


psi 


Sample 


factor of 


density, 


friction 


psi 




safety 


pcf 


angle, deg 






safety 


pcf 


angle, deg 




1 


1.948 


111.36 


39.39 


4.22 


66 


2.107 


100.08 


43.20 


2.60 


2 


1.932 


103.54 


39.44 


3.96 


67 


1.875 


114.14 


38.10 


2.30 


3 


2.124 


103.67 


38.51 


9.16 


68 


1.674 


105.11 


39.50 


.00 


4 


1.899 


115.81 


37.13 


2.40 


69 


1.904 


108.95 


36.31 


7.34 


5 


1.838 


112.50 


36.25 


2.40 


70 


1.775 


111.33 


40.98 


.05 


6 


2.008 


105.31 


36.80 


5.52 


71 


1.871 


108.26 


39.54 


2.40 


7 


1.969 


95.74 


36.42 


5.26 


72 


1.801 


122.41 


36.60 


2.60 


8 


2.137 


100.14 


44.04 


.57 


73 


1.790 


119.02 


38.60 


1.20 


9 


2.017 


103.96 


37.51 


4.74 


74 


1.964 


107.91 


41.00 


2.40 


10 


2.245 


99.51 


41.65 


3.70 


75 


1.819 


107.18 


34.80 


7.30 


11 


2.402 


102.52 


42.03 


6.30 


76 


1.913 


110.10 


39.80 


1.60 


12 


1.937 


111.54 


43.19 


.00 


77 


1.913 


105.47 


40.40 


1.20 


13 


2.009 


96.73 


36.20 


6.30 


78 


2.040 


112.15 


41.90 


2.60 


14 


1.713 


105.49 


31.90 


5.50 


79 


1.887 


110.95 


40.80 


.60 


15 


1.550 


104.15 


36.91 


.00 


80 


1.661 


114.64 


35.20 


3.30 


16 


2.246 


104.24 


43.23 


1.61 


81 


1.622 


109.11 


34.90 


2.90 


17 


2.388 


106.46 


42.78 


4.74 


82 


2.363 


119.12 


43.80 


6.90 


18 


1.820 


103.97 


34.56 


4.48 


83 


2.288 


112.54 


47.00 


.50 


19 


2.328 


109.54 


37.78 


11.25 


84 


2.030 


114.79 


45.00 


.00 


20 


2.609 


103.14 


43.77 


13.59 


85 


2.102 


106.93 


42.40 


3.40 


21 


1.909 


110.85 


39.89 


2.66 


86 


1.916 


103.65 


40.14 


1.35 


22 


2.055 


104.04 


42.71 


2.05 


87 


1.984 


104.89 


40.24 


3.96 


23 


2.169 


97.81 


44.12 


2.66 


88 


1.962 


102.07 


39.95 


3.96 


24 


2.216 


103.96 


40.59 


8.38 


89 


2.524 


113.11 


43.23 


11.51 


25 


2.134 


100.61 


42.96 


1.61 


90 


2.144 


109.08 


37.78 


10.73 


26 


2.075 


102.06 


42.82 


2.40 


91 


2.096 


112.27 


36.69 


11.25 


27 


1.900 


108.50 


43.10 


.00 


92 


1.771 


98.86 


41.10 


.00 


28 


1.896 


99.67 


36.28 


7.99 


93 


1.980 


100.70 


41.90 


1.80 


29 


1.812 


96.12 


39.59 


1.61 


94 


2.041 


100.83 


44.10 


.30 


30 


1.965 


105.12 


41.27 


2.14 


95 


1.802 


105.89 


41.60 


.00 


31 


2.617 


111.45 


42.90 


15.50 


96 


1.987 


107.55 


40.80 


3.20 


32 


2.194 


112.55 


44.50 


.90 


97 


2.126 


111.88 


35.60 


14.80 


33 


1.802 


104.27 


34.06 


7.73 


98 


1.940 


111.79 


43.70 


.00 


34 


1.998 


115.73 


37.82 


7.86 


99 


1.928 


100.15 


40.90 


2.10 


35 


1.981 


108.40 


35.98 


9.42 


100 


1.974 


111.59 


37.50 


7.40 


36 


1.773 


103.94 


41.13 


.00 


101 


2.212 


102.85 


43.86 


4.70 


37 


2.044 


118.10 


33.80 


15.67 


102 


2.204 


97.90 


42.91 


5.00 


38 


2.150 


112.20 


42.27 


2.40 


103 


2.110 


99.18 


41.89 


4.48 


39 


1.740 


109.56 


33.15 


7.60 


104 


1.894 


105.49 


37.56 


5.52 


40 


1.716 


114.06 


40.20 


.00 


105 


1.945 


98.80 


41.17 


2.14 


41 


2.360 


104.86 


40.60 


12.80 


106 


1.836 


111.97 


27.10 


18.79 


42 


1.602 


109.29 


31.00 


7.00 


107 


1.923 


102.53 


31.00 


15.30 


43 


1.971 


115.27 


41.30 


1.30 


108 


1.574 


111.19 


31.80 


5.50 


44 


2.028 


101.66 


39.80 


5.50 


109 


1.960 


101.19 


36.10 


9.70 


45 


1.674 


113.76 


39.50 


.00 


110 


2.098 


104.65 


39.70 


7.10 


46 


2.441 


108.66 


45.30 


6.20 


111 


1.742 


111.58 


35.80 


4.40 


47 


2.033 


106.11 


41.10 


1.90 


112 


1.547 


107.24 


37.30 


.00 


48 


2.228 


106.41 


40.50 


8.80 


113 


1.508 


106.87 


36.60 


.00 


49 


2.199 


114.94 


42.20 


5.70 


114 


1.340 


107.74 


29.50 


2.90 


50 


1.809 


114.08 


41.70 


.00 


115 


1.793 


98.32 


38.20 


2.80 


51 


1.771 


96.29 


41.10 


.00 


116 


1.517 


102.58 


26.80 


10.50 


52 


1.975 


102.36 


36.80 


8.12 


117 


2.137 


99.20 


40.90 


6.30 


53 


2.170 


98.83 


41.22 


6.56 


118 


1.570 


99.17 


30.80 


7.20 


54 


2.041 


100.47 


41.99 


2.92 


119 


1.798 


111.45 


37.30 


3.70 


55 


1.460 


111.94 


31.40 


3.40 


120 


1.938 


112.07 


40.50 


2.40 


56 


1.868 


109.85 


36.60 


6.20 


121 


1.983 


105.09 


41.00 


2.90 


57 


1.816 


108.53 


38.70 


1.00 


122 


1.633 


112.18 


25.90 


15.00 


58 


1.884 


109.03 


39.80 


2.30 


123 


1.473 


114.27 


28.70 


6.80 


59 


1.847 


104.07 


42.30 


.00 


124 


2.057 


112.02 


41.40 


4.20 


60 


1.826 


107.41 


39.20 


1.10 


125 


2.063 


108.98 


38.20 


8.40 


61 


1.603 


106.65 


38.30 


.00 


126 


2.418 


107.78 


46.60 


1.90 


62 


1.816 


109.90 


38.30 


2.80 


127 


2.181 


106.15 


44.40 


1.20 


63 


1.679 


109.93 


39.60 


.00 


128 


1.476 


110.83 


33.00 


1.90 


64 


2.028 


102.86 


41.10 


1.80 


129 


2.154 


100.33 


46.70 


.00 


65 


2.013 


99.50 


40.60 


4.20 


130 


1.740 


94.96 


40.60 


.00 



INT.-BU.OF MIN ES,PGH.,P A. 26Q9E 



A" • 





v 6 ^ 











» ^ 










s* <y ^amSb * ^p & *• 










'* o. 






4> > 



4<2* 







O. ' . „ o 



^ .: 







^6^ 



V c*J^w«' °^ 4P 










.S^r 











Q_ * 



.■» o 




>^ *1*°* 









k V^u 













*bV" 



^ -v 



"of 



















^^ 



.^ ♦: 






\f 



-o *r.T*-A ^ *-"^T ,, .G*' ^t k "*•'•» ,, "i0 , 



•o V 




'J * ;, 






*w 



A°+ .1 



»p*\. 



l '- ^^ ^^&: W •JS'' ^/ -Wife w ; Jsfe^ ***** 











^^ 



v* 3 



*w 







^ v 

















& \<f' SjMjfc* ' \<? ' - % MM % '\***' : *Mm° ****** ' :%l 









>0 




«5°^ - 




1> 6«_-«* 



*S?^V %^'\S %' 7 ^ ; '^ \ ,; ^Y 











w 








• ^o^ . 



»°v '. 



^°* . 












&* ^-."'••••\0' <*"*^7V^*.G* ^."'••»* 4 ^ V <». **5tv^ , .6 - *' ^*.*' , "»* 4 ^ 









^**6* 3". ^-6* 



